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THEORETICAL  AND   PRACTICAL  TREATISE 


ON 


ASTIGMATISM 


BY 


SWAN    M.    BURNETT,  M.  D., 

Professor  of  Ophthalmology  and  Otology    in    the    University    of    Georgetown , 

Ophthalmic  and   Aural  Surgeon    to    the    Garfield   Hospital,   and 

Director  of  the  Ophthalmic   and  Aural  Clinic  at  the 

Central    Dispensary    and    Emergency 

Hospital,  Washington,  D.  C. 


WITH     FIFTY-NINE     DIAGRAMS     AND     ILLUSTRATIONS. 


1887. 

J.  H.  CHAMBERS  &  CO., 

PUBLISHERS  AND  DEALERS  IN  MEDICAL  BOOKS, 

3fr.  Louis,  Mo. 


COPYRIGHTED    1887    BY  J.  H.  CHAMBERS. 
ALL   RIGHTS   RESERVED. 


1.981 

TO    THE     READER. 


The  addition  of  one  more  medica)  book  —  even  though  it  be 
a  small  one  —  to  the  scores  that  are  annually  issued  from  the 
press,  carries  with  it  a  demand,  on  the  part  of  the  reading  pub- 
lic, for  its  raison  d'etre. 

The  cause  of  the  existence  of  this  little  work  has  its  founda- 
tion in  my  own  needs  as  developed  in  my  studies  of  refractive 
anomalies,  and  in  my  conception  of  the  needs  of  others  as 
manifested  to  me  during  the  last  eight  years  as  a  teacher  of 
general  and  special  students  and  general  practitioners. 

An  examination  into  the  statistics  of  eye-affections  shows 
that  the  various  anomalies  of  refraction  form  about  one-third 
of  the  whole  number  of  eye  cases  presenting  themselves  for 
treatment  in  private  practice,  and  of  these  two-thirds,  or  about 
2OC/C  of  the  whole,  suffer  from  astigmatism  in  an  appreciable 
degree. 

No  one,  then,  I  think,  will  deny  to  astigmatism  the  worth  of 
a  treatise  special  to  itself,  particularly  when  there  is  taken  into 
consideration  the  great  difficulty  encountered  in  clearing  away 
the  perplexities,  uncertainties  and  paradoxical  manifestations 
which  enshroud  many  cases  of  the  anomaly,  and  which  are  the 
despair  of  the  beginner  in  refraction  studies.  - 

And,  while  fully  aware  that  Time  and  Patience  are  two  most 
important  and  indispensible  factors  in  unraveling  the  tangled 
threads  of  evidence,  it  cannot  be  doubted  that  nowhere  in  the 
whole  range  of  medical  practice,  is  accurate  knowledge,  based 
on  positive  science,  of  such  avail  as  in  the  diagnosis  of  astigma- 
tism. To  lead  to  such  accurate  knowledge  through  the  paths 
of  positive  science  has  been  the  chief  incentive  to  my  labor. 

The  preliminary  chapter,  embracing  the  fundamental  prin- 
ciples of  optics  which  are  needed  for  a  clear  comprehension  of 
what  follows,  was  introduced  because  experience  shows  that 


IV  TO    THE    READER. 

most  students  of  medicine  in  this  country  are  lacking  in  such 
knowledge.  No  one  can  more  fully  realize  than  I  the  almost 
impossible  task  of  giving  a  concise  yet  perfectly  clear  exposi- 
tion of  optics  in  a  single  chapter.  Those,  therefore,  to  whom 
my  work  appears  not  sufficiently  elementary,  I  would  refer  to 
the  appendix  to  Dr.  Loring's  "Text-book  of  Ophthalmoscopy," 
and  to  a  most  excellent  and  remarkably  simple  and  lucid 
"Treatise  on  Simple  and  Compound  Ophthalmic  Lenses,"  by 
Chas.  F.  Prentice,  of  New  York,  where  they  will  find  the  sub- 
ject treated  of  in  the  simplest  form  possible,  while  those  desir- 
ing a  fuller  application  of  these  laws  will  do  well  to  consult  the 
first  part  of  the  translation  of  Dr.  Landolt's  treatise  on  the 
"  Refraction  and  Accommodation  of  the  Eye ;"  three  works 
published  since  this  treatise  has  been  in  type. 

One  word  in  regard  to  the  bibliography.  Without  asking 
any  undue  indulgence  for  its  imperfections  and  shortcomings* 
we  would  call  to  the  mind  of  the  captious  critic  the  apothegm 
of  an  old  and  experienced  bibliographer:  "If  a  man  have  a 
pride  of  accuracy,  and  desires  to  be  cured  of  it,  let  him  make  a 
bibliography." 

I  trust  that  our  labors  in  this  regard  may  not  be  without  value, 
particularly  to  the  future  writer  on  the  subject,  for  we  believe 
that,  in  that  far  away  time,  should  the  New  Zealander,  prowl- 
ing among  the  ruins  of  the  great  medical  library  on  the  banks 
of  the  Potomac,  stumble  on  a  copy  of  this  work,  he  will  find 
recorded  there  the  title  of  every  important  paper  on  the  subject 
that  has  appeared  up  to  the  year  of  Grace  1886. 

I  desire  to  return  publicly  my  acknowledgment  of  valuable 
assistance  in  the  construction  of  the  work — the  bibliography 
in  particular  —  received  from  my  former  assistant,  Dr.  Louis 
Kolipinski. 

SWAN    M.  BURNETT. 

1734  K  ST.,  WASHINGTON, 
January,   1887. 


TABLE     OF     CONTENTS. 
CHAPTER  I. 

Definition  of  astigmatism — Fundamental  laws  of  optics — Re- 
fraction by  spherical  surfaces — Formation  of  images  by 
convex  refracting  surfaces — Test  glasses  and  their  number- 
ing. -  1-13 

CHAPTER  II. 

Refraction  by  ellipses,  spheroids  and  ellipsoids — Focal  Interval 
of  Sturm — Character  of  the  focal  lines — Cylindrical 
glasses.  H-37 

CHAPTER    III. 

Astigmatism  in  the  human  eye — History  of  corneal  astigma- 
tism— The  different  forms  of  ametropia — Varieties  of  as- 
tigmatism. 38-54 

CHAPTER    IV. 

Diagnosis  of  astigmatism — Determination  of  its  form  and  de- 
gree and  the  direction  of  its  principal  meridians.  5  5-62 

CHAPTER    V. 

Difficulties  and  obstacles  in  the  way  of  an  accurate  diagnosis 
of  astigmatism — Influence  of  accommodation — The  use  of 
mydriatics.  -  63—73 

CHAPTER    VI. 

Other  subjective  methods  of  examination — Change  in  the  form 
of  a  point  of  light — Adaptation  of  Scheiner's  experiment 
— The  Stenopaic  slit — Modifications  of  Snellen's  fan — Op- 
tometers.  74-88 


VI  CONTENTS. 

CHAPTER  VII. 

Objective  methods  of  examination — The  ophthalmoscope  as  a 
means  of  diagnosis  in  astigmatism.     -  89-114 

CHAPTER  VIII. 
Skiascopy  (the  shadow-test.)  1 15-123 

CHAPTER    IX. 
Keratometry  and  keratoscopy.       -  124-138 

CHAPTER  X. 
Symptoms  of  astigmatism.  139-146 

CHAPTER    XI. 
Causes  of  astigmatism — Lenticular  astigmatism.  -          147-154 

CHAPTER  XII. 

Correction  of  astigmatism.  155-176 

CHAPTER    XIII. 

Irregular  astigmatism — Conical  cornea.     -  177-204 

Note  to  Section  196;  pp.  170-171.  203-205 

Appendix — A  statistical  record  of  806  astigmatic  eyes.  206-231 


LIST    OF    ILLUSTRATIONS    AND    DIAGRAMS. 


Fig.  1.    -Different  forms  of  spherical  lenses                         -  2 

Fig.  2. — The  formation  of  a  spherical  plano-convex  lens  3 

Fig.  3. — Refraction  of  rays  by  a  simple  convex  surface        -  5 

Fig.  4. — Cardinal  points  of  a  bi-conxex  lens  6 

Fig.  5. — An  image  formed  by  a  convex  refracting  surface  -  8 

Fig.  6. — An  ellipse  15 

Fig.  7. — Refraction  by  the  sharper  end  of  an  ellipse  17 

Fig-  8. — Refraction  by  the  blunter  end  of  an  ellipse      -  18 

Fig.  9. — Refraction  by  a  spheroid      -                                       -  19 

Fig-  10. — Lines  formed  by  the  normals  to  a  triaxial  ellipsoid  21 

Fig.  11. — Character  of  the  focal  lines  in  a  triaxial  ellipsoid  24 

Fig.  12. — Sections  of  Sturm's  interval  at  its  various  parts  27 

Fig.  13.— Formation  of  the  focal  interval  of  Sturm  -            -  28 

Fig.  14. — Formation  of  a  cylindrical  lens  3o 

Fig.  15. — Refraction  by  a  cylindrical  lens    -                         -  31 

Fig.  16. — A  concave  cylinder      -  31 

Fig.  17. — The  elliptical  form  of  the  cornea  -                          -  40 

Fig.  18.- — Form  of  the  focal  curve  of  the  normal  cornea  41 

Fig.  19. — Emmetropic  and  ametropic  eyes  compared             -  49 
Fig.  20. — Diagrammatic  representation  of  the  direction  of 

the  axis  of  an  astigmatic  meridian       -  58 
Fig.  21.  —  Method  of  recording  a  case  of  compound  astig- 
matism -  59 
Fig.  22. — Distant  point  of  light  as  seen  by  an  astigmatic  eye  75 
Fiir.  2M. — Schemer's  experiment  78 
Fig.  24.— Test-types  of  Pray  82 
Fig.  25. — The  clock-face  of  Green.  84 
Fig.  20. — Direct  method  of  examination  with  the  ophthal- 
moscope 91 
Fig.  27. — Jager's  inaccurate  drawing  of  the  fundus  of  an 

astigmatic  eye   -  95 
Fig.  28. — Appearance  of  the  fundus  ot  an  astigmatic  eye  as 

seen  in  the  direct  method  of  examination    -            -  97 
Fig.  29. — Refraction  ophthalmoscope  with  a  clip  for  the  in- 
sertion of  cylindrical  lenses       -  100 
Fig.  30. — Formation  of  the  actual  inverted  image  in  the  in- 
direct method  of  ophthalmoscopic  examination       -  101 
Fig.  31.  —Change  in  the  size  and  position  of  the  real  image 
of  the  hypermetropic  eye  in  the  indirect  method 
of  ophthalmoscopic  examination  103 


Viii  LIST   OF    ILLUSTRATIONS    AND    DIAGRAMS. 


Fig.  32. — How  the  real  image  of  the  myopic  eye  varie-   in 
size  on  removal  of  the  auxiliary  lens,  in  the  indi- 
rect method  of  examination  -   1"± 
Fig.  33. — Fondue  of  an  eye  with  mixed  astigmatism,  when 

the  auxiliary  Ions  is  held  close  to  the  cornea    •  1(I7 

Fig.  34. — Same,  where  the  auxiliary  lens  is  at  a  great   di- 

t  a  nee  from  the  cornea  1"^ 

Fig.  35. — Optical  principles  on  which skiascopy  is  base- 1         1  It; 
Fig.  36. — How  the  shadow  in  skiascopy  moves  across  the 

pupil  when  the  meridians  in  astigmatism  are  oblique   1  ~2 1 
Via.  37. — The  ophthalmometer  (keratometer)  of  Javal  and 

Schiotz  (after  Java  1,  126 

Fig.  38. — Appearance  of  the  corneal  image  of  the  bands  in 

tin- keratometer  (after  Javal)  -  130 

Fig.  3!).— The  keratoscope  of  Placido 

Fiir.  40. — Wecker' square  (after  Wecker)      -  -135 

Fig.  41 .  — Figures  for  determining  the  amount  of  change  in  the 

corneal  reflection  of  Wecker's  square  (after  Wecker)  135 
Fig.  4 1'.      Mryrmvit/'s  trial  frame  (Meyrowitz)  1  •"••'> 

Fiir.  -I-"-.-    Diagram  for  recording  astigmatism  -  159 

Fig.  44. — Effect   of  a   cylindrical  lens  on  the  refraction  of 
the  sharper  end  of  an  ellipsoid  where  the  periph- 
eral rays  of  the  two  meridians  are  brought  together  166 
Fig.  45. — Another  effect  of  the  same  1»'>7 

Fig  4»">. — Refraction  by  the  blunter  and  sharper  end  of  an 

ellipsoid  corrected  by  a  cylinder  1 1^ 

Fig.  47 — Sectorial  construction  of  the  human  crystalline  lens  1  7s 
Fi«r.  4s. — Spectrum  of  the  authors  crystalline  lens  17'.* 

Fig.  4!>. — Appearance  of  a  distant  point  of  light  to   the  au- 
thor's right  eye  -   1s" 
Fig.  50. — Polyopia  monocularis  (after  Helmholtz)  1 s  1 
Fig.  51.—  Keratoseopic     appearances     in    central    corned 

opacity  -   1^4 

Fig.  52. — Same,  in  small  corneal  infiltration     -  1^:. 

Fig.  53. — Same,  in  cystoid  cicatrix   -  -185 

Fig.  54. — Same,  after  cataract  extraction  1^7 

Fig.  55. — Same,  in  ophthalmo-malacia  1^ 

Fig.  56. — Lateral  view  of  conical  cornea  (after  Wardrop)       I'.rj 
Fig.  57. — Disk  and  large  vessels  in  kcratoconus  in  the   di- 
rect ophthalmoscopic  examination       -  lie! 
Fig.  58.—  Keratoscopic  images  at   various  parts  of  a  con- 
ical cornea                                                                         -   1!»4 
Fig.  50. — Keratoscopic  images  in  conical  cornea                       1«J5 


CHAPTER    I. 


DEFINITION  OF  ASTIGMATISM — FUNDAMENTAL  LAWS  OF  OPTICS 
REFRACTION,  BY  SPHERICAL  SURFACES — FORMATION  OF  IM- 
AGES   BY    CONVEX    REFRACTING    SURFACES — TEST 
GLASSES  AND  THEIR  NUMBERING. 

§  I.  ASTIGMATISM  is  a  condition  resulting  from  any  irregu- 
larity in  the  refraction  of  an  optical  apparatus  which  renders 
impossible  the  formation  of  clear  and  distinct  images  of  ob- 
jects in  all  their  parts. 

§  2.  In  order  to  satisfactorily  study  this  irregularity  in  re- 
fraction, it  will  be  necessary  to  first  understand  those  laws 
which  have  been  found  to  govern  refraction  by  surfaces  having 
a  regular,  spherical  form. 

To  this  end  it  will  be  well  to  call  to  mind  here,  at  the  begin- 
ning, some  of  the  elementary  principles  of  optics,  since  they 
form  the  foundation  of  all  that  follows,  and  will  be  indispensa- 
ble to  beginners  for  their  further  study  of  the  subject  before  us. 
We  should  bear  in  mind  that: 

a. — From  every  point  of  an  illuminated  object  there  go  out 
luminous  rays  in  every  direction  free  to  the  passage  of  light. 

b. — These  rays  of  light  move  always  in  straight  lines,  even 
when  thrown  out  of  their  original  course  by  reflection  or  re- 
fraction. 

c. — Rays  of  light,  while  always  mathematically  divergent, 
when  they  have  arrived  at  a  distance  of  eighteen  or  twenty 
feet  from  their  source,  can  be,  for  all  practical  purposes,  con- 
sidered parallel,  and  they  remain  so  for  an  infinite  distance. 
For  the  lenses  in  common  use  in  ophthalmology,  and  for 
the  eye  itself,  therefore,  all  distances  greater  than  twenty 
feet  are  practically  infinite. 

The  laws  governing  reflection  and  refraction  are  few  and 

(52) 


2  LAWS  OF  REFLECTION  AND  REFRACTION. 

simple.  The  law  of  reflection  is  that  the  angle  of  reflection 
is  equal  to  the  angle  which  the  incident  ray  makes  with  per- 
pendicular to  the  reflecting  surface  at  the  point  of  inci- 
dence. 

The  angle  (or  amount)  of  refraction  is  governed  by  two  con- 
ditions, i)  the  angle  which  the  incident  ray  makes  with  the 
perpendicnlar  to  the  refracting  surface  at  the  point  of  inci- 
dence, and  2)  by  the  index  of  refraction  (or  density)  of  the  re- 
fracting medium. 

All  questions  in  optics,  however  complicated,  must  finally  be 
brought  into  harmony  with  these  few  general  iaws  for  their 
perfect  solution. 

As  in  astigmatism  we  have  to  do  mostly  with  refraction,  we 
shall  pass  by  any  consideration  of  the  laws  of  reflection  as  ap- 
plied to  optical  apparatus. 

Fig.  i. 


DIFFERENT  FORMS  OF  SPHERICAL  LENSES.  A,  Plano-convex.  B,  Plano-con- 
cave. C,  Double-convex.  D,  Double  concave.  E,  Convex  meniscus,  f,  Concave 
meniscus. 

§  3.  The  function  of  every  optical  appliance  is  to  change 
the  course  of  the  rays  of  light  falling  upon  it  from  a  source  of 
illumination,  and,  usually,  in  such  a  manner,  that  there  shall 
be  formed  an  image  of  some  object. 

The  optical  apparatus  with  which  we  have  to  do  in  refrac- 
tion are  called  lenses,  because  they  are  usually  of  a  shape 
somewhat  resembling  the  seed  of  a  lentil. 

Those  in  common  use  are  divided  into  two  general  classes, 
called  convex  and  concave,  according  to  the  character  of  their 
curved  surfaces.  A,\in  Fig.  i  is  a  convex  lens,  R  is  a  concave  lens. 


DIFFERENT  FORMS  OF  SPHERICAL  LENSES.  3 

In  these  it  will  be  noticed  that  one  surface  is  curved  while  the 
other  is  straight  or  plane — they  are  therefore  called  plano- 
convex and  plano-concave,  to  distinguish  them  from  those 
which  have  both  surfaces  curved  as  in  C  and  D,  and  which  are 
called  from  this  circumstance  double  (or  bf)  convex  and  double 
(or  bi]  concave  respectively.  The  forms  E  and  F  are  called 
meniscuses  because  of  their  fancied  resemblance  to  the  moon  at 
its  quarter.  In  meniscuses  both  surfaces  are  curved  in  the 
same  direction.  When  the  concavity  is  predominant  it  is  called 
a  concave  meniscus,  F;  when  the  convex  curve  is  in  excess  it  is 
called  a  convex  meniscus  t  E.  All  convex  lenses  are  also  desig- 
nated as  plus  (+),  positive  or  collecting,  and  all  concave  lenses 
as  minus  ( — ),  negative  or  dispersing. 

Fig.  2. 


f 


The  formation  of  a  Spherical  plano-convex  lens. 

It  will  be  observed  that  the  curved  surface  in  all  these  lenses 
is  regular,  like  that  of  a  globe  or  sphere,  and  for  this  reason 
they  are  called  spherical.  It  is  to  be  remembered  that  these 
drawings  represent  only  meridional  sections  of  the  lenses.  It 
is  characteristic  of  the  spherical  lens  that  the  sections  made 
in  all  its  diameters  or  meridians  are  similar,  and  therefore  the 
curvature  of  its  various  meridians  must  be  the  same. 

§  4.  All  lenses  of  this  character,  therefore,  are  sections  of  a 
sphere  as  shown  for  the  plano-convex  form  in  A  Fig.  2;  and 


4  CARDINAL    POINTS    OF    AN    OPTICAL    SYSTEM. 

the  radii  of  curvature  of  the  lens  are  the  radii  O  e ,  0  f,  etc.. 
of  the    circle  of  which  its  surface  forms  a  part. 

§  5. — The  optical  properties  of  a  refracting  system  depend 
upon  what  are  called  its  cardinal  points,  which  are  six  in  num- 
ber, namely:  two  principal  foci,  two  nodal  points  and  two  prin- 
cipal points,  all  of  which  are  situated  on  the  principal  axis  of 
the  system. 

The  first  princ ipal  focus  is  the  point  where  the  incident 
should  cross 'in  order  that  the  corresponding  emergent 
shall  be  parallel  to  the  principal  axis.  The  second  principal 
focus  is  the  point  of  crossing  of  the  emergent  rays  when  the 
incident  rays  are  parallel  to  the  principal  axis.  These  points 
are  real  or  virtual  according  as  the  refracting  surface  is  positive 
or  negative. 

The  principal  points  possess  the  following  properties :  When 
an  incident  ray,  prolonged  if  necessary,  passes  through  the 
first  principal  point,  the  corresponding  emergent  ray,  or  its 
prolongation,  passes  through  the  second  principal  point,  but 
the  incident  and  emergent  rays  are  not  parallel. 

The  nodal  points  have  this  characteristic:  that  if  an  incident 
ray  or  its  prolongation  passes  through  \\\c  first  nodal  point,  the 
corresponding  emergent  ray  coincides  with  a  straight  line  par- 
allel to  the  incident  ray  and  directed  to  the  second  nodal  point. 

The  planes  passing  through  the  principal  foci  are  called  the 
focal  planes,  and  the  planes  passing  through  the  principal  points 
are  called  the  principal  planes.  The  principal  planes  enjoy  this 
property:  The  incident  and  emergent  rays  cut  the  first  and 
second  principal  planes  in  the  points  situated  on  the  same  side 
and  at  the  same  distance  from  the  principal  axis  of  the  system. 

1\\z  first  focal  distance  is  the  interval  between  the  first  prin- 
cipal point  and  the  first  principal  focus;  the  second  focal  dis- 
ignce  is  the  distance  from  the  second  principal  point  to  the  sec- 
ond principal  focus. 

The  simplest  form  of  dioptric  system  is  a  curved  surface 
separating  two  transparent  media  having  different  indices  of 
refraction.  In  Fig.  3  MN represents  such  a  surface  with  its 
center  of  curvatuiip  at  C,  through  which  the  principal  axis  X  X' 


CARDINAL    POINTS    OF    A    SIMPLE    CONVEX    SURFACE. 


5 


passes.  On  account  of  its  limited  amplitude  the  curve  M  N  can 
be  considered  as  coinciding  with  a  plane  tangent  to  its  surface  at 
A.  It  is  evident  that  any  incident  ray,  D  7,  and  its  correspond- 
ing refracted  ray  /  G  must  cut  this  plane  at  the  same  point  7, 
therefore  the  two  principal  planes  are  one  and  the  same,  and  the 
two  principal  points  through  which  they  pass  are  one  and  the 

3- 


D 


S' 


Show  ing  the  Refraction  of  Rays  by  a  simple  Convex  Surface. 

same  and  must  coincide  with  the  apex  A  of  the    curved   surface 
M  N. 

If  we  draw  from  vS  a  line  which  passes  through  the  center  of 
curvature  at  C  it  will  be  a  normal  to  the  surface  J-/ JVat  7,  since  it 
coincides  with  one  of  the  radii  of  curvature.  Any  incident  ray, 
therefore,  following  this  direction  would,  after  it  entered  the 
second  medium,  continue  without  deviation  through  C  to- 
wards S'.  C  therefore  performs  the  office  of  the  tzvo  nodal 
points,  which  are  reduced  to  one,  and,  this  coincides  with  the  cen- 
ter of  curvature.  The  second  principal  focus  will  be  at  Ff,  be- 
cause it  is  the  point  of  crossing  of  the  emergent  ray  7  G  when 
its  corresponding  incident  ray  D  I  is  parallel  to  the  principal 
axis  XX1.  Fis  the  first  principal  focus,  because  it  is  the  point 
where  the  incident  rays  should  cross  in  order  that  the  correspond- 
ing emergent  refracted  ray  7  E  shall  be  parallel  to  the  principal 


6  CARDINAL    POINTS    OF    A    BI-CONVEX    LENS. 

axis.  The  focal  distance — that  is,  the  intervals  between  these 
focal  points  and  the  principal  points — will  depend  on  the  radius 
of  curvature  and  the  index  of  refraction  of  the  second  medium. 
The  planes  passing  through  the  focal  points  Fand  F  are  called 
the  focal  planes. 

When  the  refracting    system   is   a   bi-convex   lens   the    re- 

Fig.  4. 


CARDINAL  POINTS  OF  A  BI-CONVEX  LENS. — A"  A"7,  the  two  nodal  points.    D  2?, 
the  two  principal  planes.     O,  the  optical  center.     C  C,  Focal  points. 

lative  positions  of  the  cardinal  points  are  somewhat  different. 
The  two  nodal  points  are  found  within  the  lens  at  A'  K'  as  shown 
in  Fig.  4.  Let  5  be  an  incident  ray  which,  after  refraction, 
passes  through  0,  which  is  the  optical  center  of  the  system. 
After  it  emerges  as  a  refracted  ray,  /'  R,  it  will  assume  a  direc- 
tion parallel  to  the  incident  ray  SI.  A  prolongation  of  the 
emergent  ray  R  in  the  lens  would  strike  the  principal  axis  at 


REDUCTION    IN    THE    NUMBER    OF    CARDINAL    POINTS.  / 

K',  and  a  prolongation  of  the  incident  ray  5  in  its  original  direc- 
tion would  strike  the  principal  axis  at  K.  Thus  K  and  K! 
fulfill  all  the  requirements  of  nodal  points. 

It  has  been  demonstrated  that  any  incident  ray  striking 
the  plane  D  at  a  certain  distance  from  the  axis  will  have  a  cor- 
responding emergent  ray  cutting  the  plane  D'  at  an  equal  dis- 
tance from  the  principal  axis.  D  and  D'  therefore  fulfill  all  the 
requirements  of  principal  planes,  and  as  they  pass  through  K 
and  K'  respectively  these  points  must  coincide  with  the  principal 
points.  Therefore  the  nodal  and  principal  points  are  the  same. 

Fortunately  for  the  study  of  lenses  placed  in  air,  the  six  car- 
dinal points  can  be  reduced  to  two.  The  two  principal  and  two 
nodal  points  being  the  same,  and  the  two  nodal  points  falling 
very  close  together  they  can,  for  glasses  in  ordinary  use,  be  con- 
sidered as  coinciding  with  the  second  nodal  point;  and  where 
the  medium  is  the  same  on  both  sides  of  the  lens  the  focal 
distance  is  the  same  for  the  two  sides,  so  that  we  have  to  do 
really  with  only  the  one  nodal  point  and  one  focal  distance. 

The  focal  distance  of  a  lens,  which  is  but  the  expression  of  its 
refracting  power,  is  governed,  as  stated  in  the  previous  para- 
graph, by  its  radius  of  curvature  and  the  index  of  refraction  of 
the  material  of  which  it  is  composed.  It  has  been  found  that 
when  the  glass,  of  which  a  lens  is  made,  has  a  certain  index  of 
refraction1  (1.5)  the  focal  distance  is  just  double  the  radius  of 
curvature.  When,  therefore*,  the  lens  is  a  double  convex  or 
concave,  its  focal  distance  is  equal  to  its  radius  of  curvature. 

§  6.  The  action  of  convex  and  concave  lenses  on  light  is  of  an 
opposite  character.  Rays  after  passing  through  a  convex  lens 
tend  to  come  together  at  a  point  in  front  of  the  lens,  while  rays 
after  passing  through  a  concave  lens  diverge,  as  though  they 
came  from  a  point  behind  the  lens. 

It   is    the    office    of    all    collecting    systems  (of  which  all 

1  It  is  commonly  believed,  and  many  very  good  authorities  have  fallen  into  the 
error,  that  flint  glass  is  harder  than  crown  glass.  The  index  of  refraction  of  flint 
glass  is  higher  than  that  of  crown  glass,  but  the  lead  entering  into  its  composition 
makes  it  softer. 


8 


FORMATION  OF  AN  IMAGE  BY  A  CONVEX  REFRACTING  SURFACE. 


convex  lenses  and  the  eye  are  representatives)  to  form  at  their 
foci  small  and  inverted  images  of  extraneous  objects. 

By  the  aid  of  the  few  laws,  which  we  have  laid  down  in  the  pre- 
ceding sections,  it  is  possible  to  show  by  construction,  and  with- 
out the  help  of  any  mathematical  formulas,  how  an  image  of 
an  object  is  formed  by  a  convex  refracting  surface. 

We  have  endeavored  to  do  this  in  the  construction  of  Fig.  5. 

Let  M N  represent  a  curved  surface  separating  two  transpar- 
ent media  of  different  densities  (such  as  air  and  water),  and  for 
the  sake  of  simplicity  of  construction  and  demonstration  we 
will  assume  that  the  refracting  power  of  the  water  is  twice 

fig-  5- 


Showing  how  an  Image  is  formed  by  a  Convex  Refracting  Surface. 

that  of  air — that  is  the  index  of  refraction  (*,)  =  2.  The  center 
of  the  curved  surface  is  0,  and  Of,  O  e,  O  d,  and  every  line 
drawn  from  the  surface  through  O  are  its  radii*  A  />  is  an 
object  from  all  points  of  which  rays  proceed  in  every  direction 
towards  M  X. 

Now,  in  order  to  have  an  image  of  an  object,  the  rays  coming 
from  every  point  of  the  object  must  be  again  brought  to 
another  point,  and  it  is  the  function  of  the  curved  surface  to  do 
this. 

Let  us  take  a  bundle  of  rays  proceeding  from  the  point  .  /. 
Of  these  one  will  fall  on  the  surface  M  N  At  e,  one  at  /and  one 
at  d.  We  will  now  follow  these  rays  after  their  passage  into  the 


FORMTIOX  OF  AN  IMAGE  BY  A  CONVEX  REFRACTING  SURFACE.   9 

second  medium.  The  ray  A  /"being  perpendicular  to  the  sur- 
face and  passing  through  the  center  0  (which  is  the  nodal  point 
of  the  refracting  surface)  being,  in  fact,  but  a  prolongation  of 
the  radius  Of,  suffers  no  refraction,  but  passes  straight  on  in  the 
direction  of  iv.  The  ray  A  e,  however,  falls  upon  the  curve 
M ' N  obliquely,  and  makes  an  angle  with  the  perpendicular  g  O 
to  the  surface  at  the  point  of  incidence  e.  This  perpendicular 
is  nothing  more  than  a  prolongation  of  the  radius  O  e.  As 
stated  in  §  2,  the  amount  of  refraction  which  a  ray  undergoes 
depends  upon  the  angle  it  makes  with  the  perpendicular  to  the 
surface,  and  the  difference  in  the  refracting  power  of  the  media 
(index  of  refraction).  Observation  and  experiment  have  shown 
that  when  a  ray  passes  from  a  rarer  to  a  denser  medium,  it  is 
dm-ivn  towards  the  perpendicular,  and  in  exact  ratio  to  the 
difference  in  their  refractive  powers  as  indicated  by  the 
index  of  refraction.  This  difference  is  expressed  naturally  by 
the  difference  in  the  size  of  the  angles  made  by  the  incident  and 
refracted  rays  with  the  perpendicular.  The  size  of  an  angle  is 
usually  expressed  mathematically  by  its  sine,  and  the  index  of 
refraction  is  said  to  be  equal  to  the  difference  of  the  sines. 

In  constructing  such  a  diagram  as  Fig.  5  it  is  easy  to  meas- 
ure the  size  of  these  angles.  The  angle  of  incidence  A  e  g, 
for  example,  may  be  measured  directly  by  means  of  a  gon- 
iometer, or  with  e  as  a  center  we  can  describe  the  arc  tv,  and 
with  the  same  radius  the  arc  x'  on  the  perpendicular  g  0.  The 
line  t  h  let  fall  on  the  perpendicular  from  the  incident  ray  is  the 
sine  of  the  angle  x,  and  the  sine  of  the  angle  x'  must  be 
just  one-half  as  large — that  is  the  length  of  the  line  at  xf 
must  be  half  the  length  of  /  h,  A  line  e  m  drawn  through  e 
and  the  extremity  of  the  line  at  x'  must  then  be  the  course  of 
the  ray  A  e  after  refraction,  and  it  will  cross  the  line  a  b  at  a. 
The  course  after  refraction  of  another  ray,  A  d,  can  be  deter- 
mined by  measuring  the  sines  of  the  angles  y  and  y'  in  the  same 
manner,  and  it  will  be  found  that,  if  M  N  is  a  regular  curve  it 
will  pursue  after  refraction  the  course  d  n  and  cross  the  other 
two  rays  e  m  andfzv  at  a  also ;  a  will  therefore  be  the  focus  of 
all  the  three  rays. 


IO  TRIAL    I.KNSES. 

By  a  similar  method  of  construction  it  can  be  shown  that  all 
the  rays  going  out  from  A  and  falling  on  the  curve  M  N  be- 
tween d  and  e,  and  in  fact  anywhere  on  its  surface  will  likcu  isc 
be  brought  together  at  a.  The  point  a  must  therefore  be  the 
image  of  the  point  A  in  the  object  A  B. 

By  the  same  method  of  construction  it  can  be  shown  that 
all  rays  coming  from  the  point  C  will  be  brought  to  a 
focus  at  f,  which  will  be  the  image  of  C.  By  the  same  law 
all  rays  emanating  from  />  will  be  united  at  b  forming  there  an 
image  of  that  point ;  and  so  for  every  point  between  A  and  B  there 
will  be  a  corresponding  focus  and  image  between  a  and  b.  a  b 
will  therefore  be  the  image  of  A  B.  It  will  be  observed  that  it 
is  ///rr/'Av/and  smaller  than  the  object. 

M  N  represents  only  one  meridian  of  a  curved  surface  and  A 
B  only  the  section  of  a  plane  surface,  but  it  is  evident  that  if 
MN  were  a  spherical  surface  curved  equally  in  all  its  meridians 
a  small  and  inverted  image  of  an  object  on  the  plane  A  B  will 
be  formed  at  a  b. 

It  will  be  observed  that  with  the  exception  of  the  curve  MX 
all  the  lines  in  Fig.  5  are  straight,  and  this  in  surfaces  of  very 
limited  amplitude  can  also  be  practically  considered  as  a  straight 
line.  These  lines  in  this  figure  go  to  the  construction  of  a  large 
number  of  triangles,  and  since  we  can  always  know  the  size  of 
the  object  and  its  distance  from  the  refracting  surface,  and  the 
index  of  refraction  of  the  second  medium,  we  can,  by  the  ap- 
plication of  the  few  simple  rules  of  plane  trigonometry,  easily 
find  the  position  and  size  of  the  image  and  its  distance  from 
the  refracting  surface.1 

§  7. — In  ophthalmic  practice  a  number  of  lenses  of  different 
refracting  powers  are  used  for  the  purpose  of  determining  the 
refraction  of  the  eye  and  for  correcting  optical  anomalies. 
This  series  of  lenses  used  for  examining  the  refraction  are 
called  trial  lenses.  These  sets  are  constructed  with  a  view  to 
having  all  the  glasses  that  are  necessary  with  none  that  are 

1  The  simplest  exposition  of  the  elements  of  optics  with  which  I  am  acquainted  is 
the  little  volume  by  Prof.  Gavarret  of  Paris  on  "  Images  par  reflexion  et  refraction:" 
No  translation  has  been  published  in  English. 


THE   TWO    SYSTEMS    OF    NUMBERING    GLASSES.  II 

superfluous.  In  practice  we  seldom  have  use  for  a  lens  with  a 
focus  shorter  than  two  inches, — for  even  an  aphakial  eye  does 
not  often  need  a  lens  stronger  than  two  or  two  and  one-half  inch- 
es focus, — or  longer  than  160  inches,  since  rays  become  practi- 
cally parallel  at  the  distance  of  240  inches.  The  majority  of  trial 
cases  in  use  are  composed  of  lenses  with  various  foci  embrac- 
ing these  two  extremes.  Most  of  them  have  thirty  pairs  of 
convex  and  the  same  number  of  concave  lenses. 

It  is  advantageous  to  have  this  series  with  as  nearly  as  possi- 
ble regular  intervals  between  adjoining  numbers. 

§  8.  There  are  two  methods  of  numbering  these  lenses,  one 
the  inch,  or  old ;  the  other  the  metric,  or  new.  The  advant- 
age of  the  inch  system  is  that  it  gives  directly  the  focal  dis- 
tance of  the  lens ;  one  of  its  disadvantages  is  that  the  power 
of  the  lens  must  be  expressed  in  vulgar  fractions.  As  the 
standard  of  refracting  power  is  a  lens  with  a  focal  distance  of 
one  inch  ( 1/l) ),  and  as  the  refracting  power  of  a  lens  is  in  inverse 
ratio  to  its  focal  distance,  all  lenses  with  foci  longer  than  one 
inch  must  be  expressed  in  fractions  ;  thus  a  lens  of  twelve  inches 
focus  has  a  refracting  power  of  only  one-twelfth ;  one  of  eight- 
teen  inches,  one  eighteenth,  etc.,  etc. ;  whereas  one  of  one-half 
inch  focal  distance  would  have  a  refracting  power  of  two. 
There  are  few  people  who  can  add  and  subtract  vulgar  fractions 
without  resorting  to  pencil  and  paper,  and  this  is  a  great  incon- 
venience in  the  combinations  of  lenses  which  we  sometimes 
find  it  advantageous  to  make  rapidly  in  practice.  Another  dis- 
advantage is,  that  the  inch  has  not  the  same  length  in  all 
countries ;  so  that  a  one  twentieth  in  Prussia  or  Switzerland 
would  not  be  the  same  as  one-twentieth  in  England  and  Amer- 
ica. It  is  very  desirable,  therefore,  to  have  a  universal  uniform 
numbering  of  lenses,  whose  power  shall  be  expressed  in  whole 
numbers,  or  decimals,  so  that  they  can  be  easily  added  and 
subtracted. 

§  9.  This  we  have  in  the  metric  system.  Here  the  standard 
refracting  power  is  a  lens  with  a  focal  distance  of  one  meter, 
and  as  it  is  the  measure  of  refraction  it  has  been  called  a 
Dioptry  (  D  ).  A  lens  having  twice  the  refracting  power,  with 


12 


HOW    TO    CONVERT    ONE    SYSTEM    INTO    THE    OTHER. 


a  focal  distance  of  one-half  a  meter  (  50  cm.)  is  numbered 
2  D ;  one  with  three  times  the  refracting  power  but  one-third 
the  focal  distance  (33  cm.)  is  No.  3 ;  while  one  with  one- 
half  the  refracting  power  but  double  the  focal  distance  (two 
meters)  is  called  0.50  D;  one  with  one-quarter  the  refracting 
power,  but  four  times  the  focal  distance  (four  meters),  is  0.25  D. 

It  is  easy,  however,  to  convert  one  system  into  the  other. 
The  meter  is  about  forty  English  inches  (39.37),  so  it  is  only  nec- 
essary to  divide  forty  by  the  number  of  dioptrics  in  order  to  have 
a  close  approximation  to  the  corresponding  focal  distance  in 
inches,  thus :  2  D  =  *%  =  20  inches ;  4  D  =  4%  =  10  inches; 
5  D  =  4f/5  =  8  inches,  etc.,  etc.  On  the  other  hand,  if  you 
have  the  focal  distance  in  inches,  it  is  easy  to  find  the  number 
of  the  corresponding  D,  by  dividing  forty  by  the  number; 
thus  10  inches  =  40/)0  =  4  D,  12  inches  =  *°/12  =  3.33  D,  5  inch 
=  «»/.  =  g  D,  10  inch  =  40/>o  =  4  D. 

The  following  table  comprises  the  number  of  glasses  usually 
found  in  trial  cases  expressed  in  dioptrics,  with  their  focal  dis- 
tances given  both  in  millimeters  and  inches. 

TABLE  I. 


Number 
of 
Dioptries. 

Focal  Distance 
in 
Millimeters. 

Focal   Distance 
in 
English  Inches. 

Number 
"f 
Dioptries. 

Focal  Distance 
in 
Millimeters. 

Focal  Distance 
in 
F.nglish  Inches. 

0.25 

4OOO 

'58 

5-5 

182 

7-18 

0.50 

200O 

79 

6 

1  66 

6.6 

0.75 

'333 

1000 

52-3 
39-5 

5-  7 
8 

'43 
125 

5-64 
4-9 

1.25 

800 

31.6 

9 

in 

4-4 

1.50 

666 

26.3 

10 

100 

3-9 

'•75 

571 

22.5 

it 

9' 

3-6 

2 

500 

19.7 

12 

83 

3-3 

2.25 

444 

'7-5 

'3 

77 

3 

2.50 

400 

'5-8 

'4 

7' 

ij 

-•75 

363 

'4-33 

'5 

67 

2.6 

1    "'$9" 

333 

13.1- 

16 

62 

2-5 

,'  /   3-5 

286 

I  1.2 

'7 

59 

2-3 

4 

250 

9.9 

18 

55 

2.2 

4-5 

222 

8.8 

20 

50 

1-9 

5 

2OO 

7-9 

BIBLIOGRAPHY.  13 

In  the  following  pages,  whenever  we  shall  have  occasion  to  designate  the  power  of 
lenses  we  shall,  in  order  to  give  practice  to  the  beginner  in  the  use  of  the  two 
systems,  employ  them  indiscriminately;  the  inch  system  being  always  expressed  in 
vulgar  fractions,  and  the  metric  system  in  whole  numbers  and  decimals. 

BIBLIOGRAPHY. 


Airy,  Osmund — Geometrical  Optics,  London,  MacMillan  &  Co.,  1870. 

Bonders,  F.  C. — Anomalies  of  Accom.  and  Refract,  of  the  Eye,  with  a  preliminary 
Essay  on  Physiolog.  Optics.  N.  Syd.  Soc.  London.  1864. 

Gavarret,  J. — Images  par  Reflec.  et  par  Refract.     Paris.     1866. 

Giraud-Teulon — Nouvelle  Etude  de  la  Marche  des  Rayons  lumineux  dans  1'oeil. 
Role  de  chacun  des  mileux  diopt.  Ann.  d'Ocul.  T.  51,  p.  145.  1864. 

Guebhard,  A. — Expos,  elemt.  des  Decouvertes  d.  Gauss  et  d.  Listing  surles  points 
cardinaux  d.  Syst.  diopt.  centres.  Annal  d'Oculist.  T.  LXXXI.  P.  195.  1879. 

Haltenhoff,  G. — Apparat  z.  optisch.  Demonstrat.  Zehend.  Monatsbl.  f.  Augen- 
hlk.  XII.  P.  198. 

Helmholtz,  H. — Optique  Physiologique.  Trad,  par  E.  Javal  et  Th.  Klein.  Paris. 
1867. 

Landolt,  E. — The  Introduct.  of  the  Met.  System  into  Ophth.  R.  London  Oph. 
Hosp.  Rep.  Vol.  VIII,  p.  632.  Also  in  Zehend.  Monatsbl.  f.  Augenhlk.  XIV. 
S.  223.  1876. 

Mauthner,  L. — Vorlesungen  u  d.  optisch.  Fehler.  d.  Auges.  Wien.  W.  Braumiiller. 
1876. 

Sous,  G. — Trait.  d'Optiq.  consid.  dans  ses  rapports  avec  1'exam  de  Poeil.  Paris. 
1881. 


CHAPTER  II. 


REFRACTION  BY  ELLIPSES,  SPHEROIDS  AND  ELLIPSOIDS — FOCAL 

INTERVAL  OF  STURM — CHARACTER  OF  THE  FOCAL 

LINES — CYLINDRICAL  GLASSES. 

§  10.  When  we  come  to  deal  with  a  surface  departing,  even 
to  a  limited  extent,  from  a  spherical  form,  the  few  simple  rules 
of  refraction  laid  down  in  the  preceding  chapter  no  longer 
apply,  and  there  is  no  one  point  in  the  image  where  all  the  rays 
coming  from  any  single  point  of  the  object  meet.  From  this 
circumstance  such  a  surface  is  called  Astigmatic  (from  «,  nega- 
tive prefix,  and  v-tf.ua,  a  point.) 

§  II.  But  there  are  some  surfaces  deviating  from  the  strictly 
spherical  form  for  whose  refraction  some  rules  can  be  formu- 
lated. These  are  the  ellipsoids  (including  the  paraboloids  and 
hyperboloids).  This  is  possible  only  because  the  outlines  of 
ellipses  follow  a  regular  course  in  their  conformation.  All  other 
deviations  from  the  strictly  spherical  form  are  irregular  in  out- 
line, and  refraction  by  such  figures  is  governed  by  no  rules  that 
can  be  applied  to  a  class  of  cases. 

§  12.  For  this  reason  ASTIGMATISM  is  divided  into  two  distinct 
forms:  regular  and  irregular.  * 

§  13.  There  is  one  form  of  regular  astigmatic  surface  where 
the  curve,  instead  of  representing  the  section  of  a  sphere,  is  the 
section  of  a  spheroid,  a  figure  formed  by  the  rotation  of  an  el- 
lipse around  one  of  its  axes.  In  such  a  figure,  every  section 
parallel  to  the  axis  of  rotation  is  an  ellipse.  All  sections  of 
such  a  figure  parallel  to  the  other  axis  and  at  right  angles  to 
the  axis  of  revolution  are  circles. 

§  14.  Since  the  total  refraction  of  a  spheroid  is  represented 
by  the  sum  of  the  ellipses  into  which  it  may  be  divided,  it  is  of 

(M) 


GEOMETRICAL    CONSTRUCTION    OF    THE    ELLIPSE.  15 

fundamental  importance  that  we  study  in  some    detail   the   op- 
tical properties  of  ellipses. 

Geometrically,  an  ellipse  is  "  a  plane  curve  traced  by  a  point 
which  moves  in  such  a  manner  that  the  sum  of  the  distances 
from  the  fixed  points  is  always  the  same.  The  two  fixed 
points  are  called  the  foci  of  the  ellipse. '  \Loomis'  Analyt.  Geom., 
sd  ed.,  p.  foj.) 

Fig.  6. 


AN  ELLIPSE. — A  B,  its  Major  Axis.     C  D,  its  Minor  Axis.     F'  F,  its  Foci. 

Fig.  6  represents  such  a  figure.  A  B  is  the  diameter  or 
major  axis,  and  it  is  characteristic  of  it  that  it  passes  through 
the  foci  F  and  F  and  through  the  center  of  the  figure  0,  which 
is  the  middle  point  in  the  straight  line,  A  B,  uniting  the  two 
foci.  The  conjugate  or  minor  axis,  C  D,  is  the  diameter  per- 
pendicular to  the  major  axis  A  B  at  the  center  0. 

The  curve  A  C  P  B  P'  D  is  elliptical  because  the  sum  of  the 
distances  of  its  every  point  from  F  and  F  is  the  same.  No 
matter  at  what  place  on  its  curve  PorPr  are  found,  the  sums  of 
PF  and  P  F,  and  P  .Fand  P'F  are  always  the  same. 

It  is  evident  at  a  glance  that  refraction  by  such  a  surface 
must  differ  from  that  by  a  sphere,  since  in  a  sphere  the  radius 
of  curvature,  one  of  the  factors  on  which  the  focus  of  the  refac- 

7 

ting  surface  depends,  is  the  same  for   all   parts   of  the    curve/' 
while  in  an  ellipse  it  changes  at  each  successive  point. 

In  considering  refraction  by   an   elliptical   surface   we    shall 


l6  REFRACTION    BY  ELLIPSES. 

have  two  separate  forms  to  deal  with:  one  in  which  the  light 
falls  on  the  sharper  end  of  the  ellipse  and  in  the  direction  of 
the  major  axis  A  B;  and  the  other  where  it  falls  on  the  blunter 
end,  and  in  the  direction  of  the  minor  axis  CD. 

We  have  given  in  §  6,  the  method  for  finding  the  direction 
of  a  ray  after  refraction  by  a  spherical  surface  and  by  apply- 
ing the  same  laws  here  we  can  find  the  direction  of  any  single 
ray  after  its  refraction  by  the  surface  of  an  ellipse.  We 
have  for  that  purpose  to  know  only  two  things,  viz:  the  index 
of  refraction  of  the  refracting  medium,  and  the  angle  the  inci- 
dent ray  makes  with  the  perpendicular  to  the  surface  at  the 
point  of  incidence.  The  second  of  these  data  we  could  easily 
get  in  the  sphere,  for  we  have  only  to  prolong  the  radius  of 
curvature  to  get  the  normal  to  the  curved  surface  at  any  given 
point.  The  angle  is  then  measured  as  explained  in  §  6. 
But  in  an  ellipse  it  is  not  so  easy  to  get  the  normal  at  any 
given  point,  because  there  is  no  one  center  of  curvature  from 
which  radii  can  be  drawn.  But  there  is  a  well-known  theorem 
which  enables  us  to  do  it  quite  readily.1 

According  to  this  theorem,  all  circles  and  ellipses  whose  dia- 
meters and  major  axes  correspond  hare  the  same  subtangcnts. 
We  have  constructed  Fig.  7,  which  represents  the  sharper  end 
of  the  ellipse  in  accordance  with  this  theorem.  Let  a  b  repre- 
sent the  major  axis  of  the  ellipse  of  which  b  p  is  a  portion  ; 
from  a  as  a  center  and  a  b  as  a  radius,  draw  the  segment  r  s  of 
a  circle.  Let  i<  and  y  be  the  rays  parallel  to  the  axis  and  inci- 
dent at  k  and  /.  Through  the  points  k  and  /  draw  /  c  and  ;/  d 
perpendicular  to  a  b.  These  will  cut  the  circle  at  q  and  c-,  and 
the  normals  at  these  points  coincide  with  lines  drawn  through 
them  and  the  center  a;  and  the  lines  x  K  andy  /  drawn  at  right 
angles  to  these  normals  will  be  tangents  at  the  points  q,  c-.  Now, 
if  the  circle  and  ellipse  have  the  same  subtangents  b  u  and  b  t, 

'To  be  found  in  any  treatise  on  analytical  geometry.  Compare  Loomis'  "Ele- 
ments of  Analytical  Geometry,"  1873,  page  113.  "Since  the  subtangent  is  inde- 
pendent of  the  minor  axis,  it  is  the  same  for  all  ellipses  which  have  the  same  major 
axis;  and,  since  the  circle  on  the  major  axis  may  be  considered  as  one  of  these  ellip- 
ses, the  subtangent  is  the  same  for  an  ellipse  and  its  circumscribing  circle." 


REFRACTION    BY    THE    SHARPER    END    OF    AN    ELLIPSE.  I/ 

then  the  lines  z  u  and  w  t,  drawn  through  u  and  k  and  t  and  i 
must  be  the  tangents  to  the  ellipse  at  the  points  k  and  z,  and 
the  lines  mfand  o  e,  drawn  perpendicular  to  them,  must  be 
normals  to  the  surface  at  the  points  of  incidence,  k  and  i.  We 
have  now  all  the  requisite  data,  and  have  only  to  apply  the  law 
of  sines,  as  given  in  §  6,  in  order  to  find  the  course  of  the  rays 

Fig.  7. 


Refraction  by  the  sharper  End  of  an  Ellipse. 

ig  and  kh.  In  this  case,  in  order  to  have  the  diagram  fall  within 
reasonable  limits,  we  have  assumed  a  refracting  index  =  3. 

It  will  be  seen  at  a  glance  that  in  the  case  where  the  rays 
fall  parallel  to  the  long  axis  of  the  ellipse,  the  ray  iy,  nearer 
the  axis,  crosses  the  principal  axis,  an,  after  refraction,  in 
front  of  the  more  peripheral  ray  kv, — that  is  to  say,  we  have 
an  aberration  the  opposite  in  kind  to  that  of  an  ordinary  spherical 
surface. 

If,  however,  the  light  falls  on  the  ellipse  in  the  direction  of 
the  short  axis,  or  on  the  blunter  end,  as  we  have  it  represented 
in  Fig.  8  (which  has  been  constructed  according  to  the  same 
plan  as  Fig.  7),  we  find  that  the  more  peripherally  refracted  ray 
kp  crosses  the  principal  axis  in  front  of  the  more  centrally  re- 


IS 


ABERRATION    IN    REFRACTION    BY    ELLIPSES. 


fracted  ray  ih ;  in  other  words,  we  have  an  excess   of  the   ordi- 
nary spherical  aberration. 

It  therefore  becomes  evident,//***/  if  we  take  a  series  of  curves 
passing  over  from  the  flatter  to  the  sharper  end  of  an  ellipse,  we 
will  have  in  the  refraction,  first,  an  exaggeration  of  the  spherical 

Fig.  8. 


Refraction  by  the  blunter  End  of  an  Ellipse. 

aberration — which  id II  be  greater  in  proportion  to  the  difference 
in  the  length  of  the  major  and  minor  axes — diminishing  until  the 
curve  becomes  a  circle,  when  there  will  be  only  the  ordinary 
amount  of  spherical  aberration  ;  then,  as  the  minor  axis  becomes 
shorter,  this  aberration  will  still  further  diminish  until  it  becomes, 
for  any  chosen  rays,  practically  zero.  As  the  minor  axis  still 
further  shortens,  the  aberration  passes  over  to  an  opposite  kind, 
and  the  more  central  rays  cross  the  principal  axis  in  front  of  the 
more  peripheral,  and  this  will  increase  PARI  PASSU  with  tlic  short- 
ening of  the  minor  axis. 

It  follows  from  this  demonstration  that  deviation  from  a 
spherical  form  does  not  necessarily  involve  a  lack  of  focus  for 
some  of  the  rays,  and  that  there  is  one  form  of  ellipse  in  which 
monochromatic  aberration  is  practically  abolished. 


FOCAL    ILTERVAL    OF    THE    SPHEROID.  19 

In  every  other  form,  however,  there  is  a  failure  to  focus  all 
the  rays  in  one  point,  and  this  monochromatic  aberration  in- 
creases with  the  difference  between  the  major  and  minor  axes 
of  the  ellipse.  The  foci  of  corresponding  rays  falling  at 
equal  distances  from  -the  principle  axis  do  not  all  come  together 
forming  a  point,  but  form  a  line  on  the  principal  axis  whose 
length  will  be  in  direct  ratio  to  the  difference  between  the  major 
and  minor  axes. 

It  is  apparent,  therefore,  that  in  all  figures  formed  by  the  re- 
volution of  an  ellipse  about  one  of  the  axes,  whether  in  the  form 
of  oblate  or  prolate  spheroids,  there  will  be,  with  the  excep- 
tion of  one  particular  case,  a  monochromatic  aberration  such 

Fig.  9. 


Refraction  by  a  Spheroid. 

as  to  prevent  the  formation  of  clear  and  distinct  images  on  any 
single  focal  plane.  All  rays,  however,  as  we  have  seen,  pro- 
ceeding from  a  point  on  the  axis  will  be  united  after  refraction 
at  some  place  on  that  axis,  and  those  which  fall  on  the  refrac- 
ting surface  at  equal  distances  on  either  side  of  the  axis  at 
the  same  point,  since  the  radii  of  curvature  are  the  same 
for  all  points  equidistant  from  the  axis  of  revolution.  The 
rays  A  d  and  A  d'  in  Fig.  9  will  be  united,  in  accordance  with 
the  law  of  refraction  by  ellipses,  when  the  light  falls  on  the 
blunter  end  as  demonstrated  above,  at  h\  the  rays  A  c  and  A  c' 
at^-,  and  A  e  and  A  e'  at/,  and  so  on  for  the  whole  bundle  of  rays 
coming  from  A  and  falling  on  the  spheroidal  surface  d  d'.  The 
position  of  the  foci  will  be  in  an  inverse  order  when  d  d'  is  the 
sharper  end  of  the  ellipsoid.  If  there  were  an  object  at  A, 


2O  TRI-AXIAL    ELLIPSOIDS 

therefore,  there  could  not  be  a  distinct  image  of  all  the  points  of 
its  surface  on  any  one  plane  perpendicular  to  A  B  since  the  rays 
coming  from  each  individual  point  would  have  their  foci  on  the 
different  planes  between/and  //,  according  to  the  position  of  their 
points  of  incidence  ondd'.  In  the  place,  therefore,  of  a  focal  point 
there  is  a  focal  interval  f  h,  which  is  measured  by  the  distance 
between  the  focus  of 'the  points  of  least  and  greatest  refraction 
on  the  spheroid.  It  is  characteristic  of  refraction  by  a  spheroid 
that  while  refraction  in  all  the  meridians  is  the  same,  it  is  not 
the  same  at  all  points  of  the  same  meridian. 

Such  a  form  of  refracting  surface  has  its  nearest  representa- 
tive in  the  eye  in  certain  forms  of  conical  cornea,  but  as  this 
condition  is  raiely  met  with  in  a  typical  form,  being  nearly  al- 
ways associated  with  other  irregularities  in  refraction,  we  will 
defer  its  consideration  in  detail  until  we  treat  of  irregular  astig- 
matism. 

§  15.  Those  spheroids  formed  by  the  revolution  of  an  ellipse 
about  one  of  its  axes  are  sometimes  called  bi-axial  ellipsoids 
in  order  to  distinguish  them  from  another  form  of  ellipsoid  called 
tri-axial.  The  latter  is  also  sometimes  called  a  compressed 
spheroid,  because  if  a  spheroid  be  compressed  in  the  direction 
of  its  minor  axis  so  as  to  shorten  it  in  that  meridian,  we  would 
have  a  figure  with  a  major  axis  and  two  minor  axes,  all  of  dif- 
ferent lengths.  If  we  make  a  section  of  the  base  of  such  a 
figure,  we  have,  instead  of  a  circle  as  in  the  spheroid,  an  ellipse, 
as  shown  in  Fig.  6,  in  which  A  B  would  be  the  long  minor  axis, 
and  CD  the  short  minor  axis,  the  major  axis  passing  through  0 
and  the  apex  of  the  figure.  Moreover,  it  would  follow  that 
there  would  be  a  meridian  of  greatest  curvature  which  would 
correspond  to  the  shorter  minor  axis,  and  a  meridian  of  least 
curvature  which  would  correspond  to  the  longer  minor  axis.  It 
is  further  apparent  that  these  f;c<>  meridians  must  be  at  right 
angles  to  each  other. 

Refraction  by  an  ellipsoid  with  such  an  irregular  sur- 
face is  much  more  complicated  than  that  by  a  sphere  or  spher- 
oid, and  it  is  impossible  to  formulate  any  laws  in  regard  to  it 
that  will  apply  to  the  surface  as  a  whole. 


MERIDIANS    OF    A    TRI-AXIAL    ELLIPSOID. 


21 


In  the  spheroid,  the  minor  axis  being  the  same  for  all  the 
meridians  of  the  surface,  all  rays  falling  at  equal  distances  from 
the  principal  axis  are  brought  together  at  the  same  point  on  the 
optical  axis,  as  shown  in  §  14  (Fig.  9).  When,  however,  the  minor 
axis  is  different  for  the  two  principal  meridians,  as  in  Fig.  6, 
this  can  no  longer  be  the  case,  and  only  those  rays  falling  in 
the  principal  meridians  are  united  on  the  optical  axis,  and  even 
these  will  not  all  be  at  the  same  point.  The  rays  falling  in  the 
other  meridians  are  scattered,  and  when  meeting  at  all,  cross  at 
some  point  off  the  optical  axis. 

Fig.  10. 


LINES  FORMED  BY  THE  NORMALS  TO  A  TRI-AXIAL  ELLIPSOID.  A  Af  and  B  B'  are 
the  principal  meridians.  The  curved  lines  C  Cf  and  D  D'  represent  the  position  of 
the  normals  in  two  intermediate  meridians.1 

This  scattering  of  the  rays  is  due  to  the  peculiar  "  skew  " 
form  of  the  refracting  surface,  which  changes  its  curvature  at 
each  successive  point,  so  that  normals  to  the  surface,  (which,  as 
we  have  seen  in  §  4,  control  the  direction  of  the  refracted 
rays )  fall  in  the  same  plane  only  in  the  two  principal  meridians 

1  This  condition  can  be  very  effectively  shown  on  a  model  of  a  triaxial  ellipsoid 
made  in  wax.  Pins  are  stuck  in  rows  corresponding  to  the  various  meridians,  each 
pin  being  perpendicular  to  the  surface  and  representing  a  normal  at  that  point.  It 
will  be  seen  on  an  inspection  of  these  rows,  that  none  except  those  corresponding  to 
the  principal  meridians  form  straight  lines.  All  the  others  are  curved,  no  two  points 
lying  in  the  same  plane  passing  through  the  apex  of  the  figure.  Fig.  10  represents 
in  C  Cf  and  D  D'  the  curve  of  two  intermediate  meridians,  projected  on  a  plane  sur- 
face. Dr.  Knapp  was  the  first,  I  believe,  to  construct  such  a  model. 


22  FOCAL  INTERVAL  OF  STURM. 

as  shown  at  A  A',  and  B  B' t  Fig.  10.  Normals  to  all  the  other 
meridians  do  not  fall  in  the  same  plane  forming  right  lines  like 
E  E'  and  FF,  but  each  one  falling  in  a  different  plane  make 
a  line  curved  as  in  CO  and  D D' . 

Rays  falling  in  these  meridians,  therefore,  can  not  be  brought 
to  a  focus  at  the  same  place,  since  the  refracted  rays  will  no 
longer  lie  in  the  same  plane  as  before  their  incidence.  Some 
will  cross  above  and  some  below  the  optical  axis,  but  they  can 
never  meet.  Only  those  rays  falling  in  the  principal  meridians 
and  in  the  planes  parallel  to  them  can  be  united  after  refraction, 
because  it  is  only  those  rays  which  lie  in  the  same  plane  before 
and  after  refraction. 

§  1 6.  It  is  evident,  then,  that  while  the  rays  refracted  by  such 
a  surface  can  never  meet,  at  a  single  point  there  is,  nevertheless, 
a  certain  amount  of  focussing  and  this  will  be  found  on  lines  at 
right  angles  to  the  corresponding  principal  meridians,  and  the 
planes  parallel  to  them,  by  which  the  rays  are  refracted.  As  there 
are  two  principal  meridians,  the  focus  of  a  triaxial  ellipsoid  will 
therefore  not  be  a  point,  but  two  lines  perpendicular  to  each 
other;  one  being  the  focal  line  of  the  more  strongly  curved 
meridian,  lying  nearest  the  refracting  surface  and  perpendic- 
ular to  its  corresponding  meridian ;  the  other,  the  focal  line  of 
the  meridian  of  least  curvature,  being  farthest  from  the  refract- 
ing surface  and  perpendicular  to  its  corresponding  meridian. 
The  distance  between  these  two  lines  is  called  the  focal  inten>al 
of  Sturm,  in  honor  of  his  having  first  described  it. 

In  Fig.  13,  §  1 8,  vv'  is  the  focal  line  of  the  meridian  of  greatest 
curvature  V  V,  and  //  //'  is  the  focal  line  of  the  meridian  of  least 
curvature  H  ff  ;  the  distance  m  n  between  them  is  \hzfocal  inter- 
val. 

Preliminary  to  a  further  consideration  of  the  nature  of  this 
focal  interval  we  will  study  briefly  the  character  of  the  focal 
lints  which  form  its  boundaries. 

It  is  common  with  writers  on  astigmatism  to  speak  of  the  an- 
terior and  posterior  focal  planes,  meaning  by  these  the  planes 
passing  through  the  foci  of  the  principal  meridians.  To  the  use 
of  these  terms  no  exceptions  can  be  taken  when  they  are  lim 


EXPERIMENTAL  DEMONSTRATION  OF  ASTIGMATIC  REFRACTION.        23 

ited  in  their  application  to  the  planes  passing  through  the  points 
mentioned.  When,  however,  the  focal  planes  are  considered, 
as  they  undoubtedly  are  by  many,  in  the  sense  of  planes  pass- 
ing through  the  focal  lines,  the  terms  are  misapplied. 

I  think  the  error  has  arisen  from  experimental  attempts  to 
demonstrate  the  character  of  refraction  by  an  asymmetrical 
system.  One  of  the  simplest  as  well  as  the  commonest  of  these 
methods  is  the  combination  of  a  cylindrical  and  a  spherical  lens 
to  be  described  in  §  17.  This,  indeed,  makes  an  astigmatic  sys- 
tem, inasmuch  as  there  is  no  place  where  all  the  rays  emanat- 
ing from  any  point  are  united  after  refraction,  and  in  such  ex- 
periments the  anterior  and  posterior  focal  lines  do  correspond 
approximately  with  the  planes  passing  through  the  foci  of  the 
meridians  of  the  greatest  and  least  refraction.  This  is  so  be- 
cause the  two  principal  meridians  are  regularly  curved  surfaces 
— sections  of  a  sphere — subject  to  only  the  ordinary  amount  of 
monochromatic  aberration. 

If  the  cylindrical  lens  acted  alone  we  should  have  a  series  of 
foci  on  a  right  line  parallel  to  the  axis  of  the  cylinder,  as  shown 
in  Fig.  1 5 ,  §  2 1 .  Every  set  of  parallel  rays  a  a',  c  c' ',  etc.,  are  united 
after  refraction,  each  in  its  own  plane,  which  is  perpendicular  to 
the  axis  of  the  cylinder/,  at  the  points  a",  c" ,  etc.,  on  the  line 
F F  parallel  to  the  axis/  The  rays  passing  through  the  cyl- 
inder parallel  to /would,  of  course,  suffer  no  refraction.  When, 
however,  a  positive  spherical  lens  is  added  to  this  cylinder,  it  has 
the  effect  of  uniting  those  rays  passing  through  the  cylinder  in 
planes  parallel  to  its  axis  /  and  of  advancing  the  focal  line 
F  F,  forming  the  focal  interval  of  Sturm,  bounded  by  the  ante- 
rior and  posterior  focal  lines.  In  this  instance  these  lines  are 
approximately  straight,  because  the  surfaces  of  both  the  cylin- 
drical and  spherical  lenses  are  regularly  curved,  and  the  difference 
between  the  refraction  of  the  central  and  peripheral  portions 
is  expressed  by  the  usual  amount  of  spherical  aberration.  That 
is  to  say,  there  would  be  a  slight  curving  of  the  focal  lines,  their 
concavity  being  toward  the  refracting  surfaces. 

The  conditions  are  not,  however,  the  same  when  we  come  to 
deal  with  an  ellipsoid  of  three  unequal  axes.     Here  each  of  the 


FOCAL   LINES   OF   A   TRI-AXIAL   ELLIPSOID. 


meridians  is  not  the  section  of  a  sphere,  but  an  ellipse  which 
changes  its  curve  at  each  successive  point.  No  lenses  with 
such  surfaces,  so  far  as  my  knowledge  extends,  have  been  used 
in  making  these  experiments. 

It  is  very  easy,  however,  to  picture  in   the   mind's   eye   the 
conditions  we  should  have  in  refraction  by  such  a  surface.    We 


Fig. 


Showing  the  character  of  the  Focal  Lines  in  refraction  by  a  Tri-axial  Ellipsoid. 

can  imagine  the  ellipsoid  cut  into  a  series  of  adjacent 
planes  parallel  to  one  of  the  principal  meridians.  Each  of  these 
planes  will  then  represent,  as  does  the  principal  meridian  to 
which  it  is  parallel,  an  ellipse.  This  is  shown  in  V,  Fig.  1 1 , 
where  the  ellipsoid  is  divided  into  a  series — I,  2,  3,  4,  5,  6,  etc. 
— of  ellipses  parallel  to  the  principal  vertical  meridian  •:•  a 

It  must  be  evident,  when  we  consider  the  form  and  the  rela- 
tion of  these  ellipses  to  each  other,  that  there  will  have  to  be  a 


FOCAL    LINES    OF    A    TRI-AXIAL    ELLIPSOID.  2$ 

wonderful  combination  of  happy  circumstances  in  order  to  have 
the  foci  of  rays  refracted  by  all  to  lie  in  the  same  vertical  plane. 

The  foci  will  all  lie  in  the  same  horizontal  plane  because  the 
apices  of  the  ellipses,  c,  e,  o,  (which  are  the  principal  points  of 
the  refracting  ellipses,)  are  all  found  in  the  same  plane  a  h' ,  with 
the  apex  a  of  the  ellipse  I,  which  is  the  principal  meridian  to 
which  they  are  parallel ;  and  since  all  the  cardinal  points  must 
lie  in  the  same  plane,  the  foci  will  be  found  somewhere  on  the 
prolongation  of  the  horizontal  plane  passing  through  a  h'. 

But  it  is  also  very  evident  from  this  construction  that  the 
principal  points  can  not  lie  in  the  same  vertical  plane,  for  the 
apices,  a,  c,  e,  o,  of  the  several  ellipses,  I,  2,  3,  etc.,  form  part  of 
a  curved  line  which  constitutes  the  ellipse  representing  the  hor- 
izontal principal  meridian,  h  h' ,  at  right  angles  to  the  principal 
vertical  meridian  to  which  they  are  parallel,  as  shown  in  H, 
Fig.  n. 

Now,  the  position  of  the  focus  of  any  one  of  these  ellipses  in 
relation  to  the  focus  of  the  principal  meridian  depends  upon  two 
things ;  first,  upon  the  radius  of  its  curvature  as  compared  to 
that  of  the  principal  meridian  ;  and,  secondly,  upon  the  position 
of  its  principal  point  (from  which  its  focal  distance  is  measured) 
as  compared  with  that  of  the  principal  meridian.  These  rela- 
tions, again,  depend  upon  the  relations  which  exist  between  the 
three  axes  of  the  ellipsoid.  Thus,  the  curve  of  the  horizontal 
meridian  h  h'  in  H,  Fig.  n,  formed  by  the  principal  points,  a, 
c,  e,  o,  etc.,  of  the  vertical  ellipses,  will  depend  upon  the  relative 
lengths  of  the  antero-posterior  and  horizontal  axes,  whereas  the 
curvature  of  the  ellipses  themselves,  on  which  their  foci  depend, 
will  be  governed  by  the  relation  between  the  antero-posterior 
and  the  vertical  axes. 

Let  us  take,  as  an  example  to  illustrate  our  meaning,  the 
case  where  rays  fall  on  the  sharper  end  of  the  ellipsoid,  or  in 
the  direction  of  the  major  axis,  and  let  us  assume  that  the  ver- 
tical meridian  is  the  more  strongly  curved,  and  that  the  ellipsoid 
is  divided  into  a  series  of  ellipses  parallel  to  the  vertical  meridi- 
an. It  is  apparent  that  these  ellipses  become  constantly 
smaller,  with  shorter  radii  of  curvature,  as  they  pass  toward  the 


26  FOCAL    LINES    OF    A    TRI-AXIAL    ELLIPSOID. 

periphery  from  the  principal  meridian,  for  they  finally  disappear 
as  a  point  at  the  apex  //'  of  the  ellipse  on  the  blunter  end  of  the 
ellipsoid.  The  effect  of  this  would,  of  course,  be  a  constant 
shortening  of  the  focal  distance.  But  at  the  same  time  there  is 
a  constant  recession  of  the  principal  points,  c,  e,  o,  from  the 
principal  plane  of  the  principal  vertical  meridian  passing  through 
a,  with,  of  course,  a  concomitant  recession  of  the  foci. 

Now,  if  we  can  have  such  a  nice  adjustment  of  the  three  axes 
that  these  two  conditions  shall  neutralize  each  other,  the  line 
formed  by  the  focal  points  of  the  series  of  ellipses  will  be  a 
right  line,  falling  in  a  vertical  plane  passing  through  the  princi- 
pal focus  of  the  principal  vertical  meridian.  There  is,  therefore, 
one  possible  form  of  ellipsoid,  and  only  one,  in  which  the  focal 
line  of  one  of  its  meridians  will  be  a  straight  line  and  lie  in  the 
plane  passing  through  the  focus  of  the  vertical  meridian.  When- 
ever there  is  any  deviation  from  this  form  of  ellipsoid,  the  focal 
line  will  no  longer  be  straight,  but  curved,  and  the  direction  of 
its  curvature  will  depend  on  the  predominating  influence  of  the 
one  or  the  other  of  the  above-named  factors.  If  the  relation 
between  the  major  and  the  horizontal  axis  is  such  as  to  cause 
the  setting  back  of  the  principal  points  to  be  the  more  power- 
ful, then  the  curve  would  be  backward,  as  shown  at  x' ,  Fig.  1 1; 
should  the  relation  of  the  axes  be  such  that  the  shortening  of 
the  foci  would  be  in  excess,  then  the  curve  would  be  in  the  op- 
posite direction,  or  forward,  as  shown  at  x.  It  follows,  also, 
from  what  has  been  demonstrated,  that  in  no  triaxial  ellipsoid 
can  such  a  relation  between  the  axes  exist  as  to  cause  both  the 
focal  lines  to  be  straight ;  for,  as  we  have  seen,  there  is  only  one 
relation  of  the  ellipses  that  can  bring  about  such  a  result,  and 
as  from  the  very  nature  of  the  figure  the  ellipses  in  the  two 
meridians  must  be  different,  if  one  has  this  form  the  other  can- 
not have  it. 

It  is  not  possible  to  obtain  any  general  formula  which 
would  apply  to  all  forms  of  ellipsoids.  It  will  be  necessary  to 
treat  every  form  (of  which  there  is  an  almost  infinite  number) 
separately,  and  as  the  task  is  a  tedious  and  by  no  means  an  envi- 
able one,  it  would  hardly  be  worth  while  to  undertake  it  unless 
for  some  special  case. 


DEMONSTRATION  OF  THE  FORM  OF  STURM  S  FOCAL  INTERVAL.  2/ 

§  17.  The  focal  interval  of  Sturm,  as  stated  in  §  16,  is 
the  space  bounded  by  the  anterior  and  posterior  focal  lines 
which  we  have  just  considered  as  formed  by  the  foci  of  the 
meridians  of  greatest  and  least  refraction. 

The  direction  taken  by  the  refracted  rays  in  their  passage 
through  this  interval  is,  owing  to  the  conformation  of  the  refract- 
ing surface  peculiar  and  erratic,  but  it  has  been  analyzed 
sufficiently  to  enable  us  to  unravel  some  of  its  complications  and 
'to  understand  the  general  character  of  figure. 

Its  general  features  are  made  manifest  by  means  of  the  ex- 
periment with  a  combination  of  spherical  and  cylindrical  lenses, 
alluded  to  in  §  16.  Place  in  front  of  the  milk-glass  shade  of 

Fig.  12. 


Showing  the  sections  of  Sturm's  Interval  at  its  various  parts. 

a  lamp  a  diaphragm  with  a  perforation  I  mm.  in  diameter. 
This  will  serve  as  a  point  of  light,  an  image  of  which  is  formed 
on  a  movable  screen,  by  means  of  a  -f~4  or  +5  spherical  lens. 
This  image  will  be  another  round  point  of  light  as  at  A,  Fig. 
12.  Now  place  in  front  of  the  spherical  a  +i  cylindrical  lens, 
axis  horizontal.  The  round  point  of  light  will  be  immediately 
changed  into  a  sharp  vertical  line  (B]  with  ill-defined  ends. 
This  line  is  formed  by  the  rays  which  pass  through  the  spheric- 
al lens  in  the  horizontal  meridian  unaffected  by  the  cylinder. 
Those  that  pass  through  the  cylinder  in  the  vertical  meridian 
cross  and  are  scattered  before  they  reach  the  screen.  Advanc- 
ing the  screen  towards  the  combination  of  lenses,  we  have  first 
a  vertical  oval  (C),  then  a  shorter  but  broader  oval  (D],  and 
then  a  circle  (E),  all  of  which  have  ill  defined  edges,  for  at  none 
of  these  points  are  any  of  the  rays  properly  focussed.  Advanc- 


28  FOCAL  INTERVAL  OF  STURM. 

ing  the  screen  still  further  we  have  a  horizontal  oval  (F),  which 
lengthens  out  at  G,  and,  finally,  when  the  screen  is  in  the  focus 
of  the  vertical  meridian  of  the  system  we  have  again  a  line  (//) 
horizontal,  because  it  is  formed  by  the  rays  passing  through 
the  vertical  meridian. 

Astigmatic  refraction  can  also  be  shown  by  models  made  of 
thread,  the  first  of  which  was  constructed  by  Knapp,  and  by 
the  direct  observation  of  the  refracted  rays  through  water  hold- 
ing crystals  of  eocine  or  other  fluorescent  bodies  in  suspension. 

§  1 8.  All  of  these  experiments  and  models  show  the  form  of 
focal  interval  given  in  Fig.  13.  Here  V  V  represents  the  ver- 
tical and  H  H'  the  horizontal  meridian.  The  rays  refracted  by 

fig-  13- 


Showing  the  manner  of  formation  of  the  Focal  Interval  of  Sturm. 

V  V  are  brought  to  a  focus  at  m,  and  those  rays  falling  in  the 
planes  parallel  to  it  are  focussed  on  the  horizontal  line 
forming  the  anterior  focal  line  of  the  interval.  These  rays, 
after  meeting,  diverge  in  the  direction  of  h  h' .  The  rays  re- 
fracted by  the  horizontal  meridian  ////'pass  the  line  ri-'  before 
meeting,  forming  its  limits,  and  finally  are  brought  together  at 
n  on  the  vertical  line  //  //'.  All  the  rays  falling  in  planes  paral- 
lel to  H  H'  likewise  find  their  foci  on  this  line,  which  is  the 
posterior  focal  tine  of  the  interval,  and  its  limits  are  the  continu- 
ation of  the  rays  that  have  been  refracted  by  V  V  and  have 
crossed  at  v 

If  this  interval  be  divided  by  sections  perpendicular   to    the 


FOCAL  INTERVAL  OF  STURM.  2g 

axis  X  X'  we  shall  have  the  forms  represented  at  the  lower  part 
of  Fig.  13.  The  figures,  it  will  be  seen,  are  the  same  as  those 
obtained  in  the  experiment  with  the  combination  of  spherical 
and  cylindrical  lenses  shown  in  Fig.  12. 

We  first  have  at  the  focus  of  the  most  strongly  refracting 
meridian  v  v',  the  anterior  focal  line,  which  is  horizontal  and  at 
right  angles  to  its  refracting  surface.  This  gradually  merges 
into  an  ellipse  g  r  t  s,  whose  long  axis,  g  t,  is  horizontal;  this 
then  gradually  passes  into  a  circular  figure  o  e;  then  passes 
into  an  ellipse  pi  df  with  its  long  axis  vertical;  and,  finally, 
by  a  gradual  decrease  in  its  short  and  increase  in  its  long  axis, 
it  merges  into  the  posterior  focal  line  h  h' ,  which  is  vertical,  be- 
ing at  right  angles  to  its  corresponding  refracting  meridian, 
H  H'. 

§  19.  It  will  be  discovered  on  a  study  of  these  figures:  first, 
that  the  anterior  is  shorter  than  the  posterior  focal  line. 
This  is  due  to  the  fact  that  in  the  two  similar  triangles  v  v'  n 
and  h  h'  m  with  a  common  altitude  n  m,  the  angle  //  opposite 
to  v  v'  is  smaller  than  the  angle  m  opposite  to  h  h' .  This  must 
always  be  the  case,  since  the  angle  h  m  h' ,  being  the  opposite 
internal  angle  of  y  m  y'  is  larger  than  v  n  v'.  It  follows,  more- 
over, for  the  same  reason,  that  the  difference  in  the  size  of  these 
angles,  with  a  consequent  difference  in  the  length  of  their  op- 
posing sides,  must  increase  with  the  lengthening  of  the  focal 
interval.  Second,  the  circular  section  of  the  figure  will  not  be 
found  as  is  represented  in  all  the  figures  of  the  interval  I  have 
seen,  except  those  given  by  Mauthner,  and  as  it  is  actually  de- 
scribed as  being  by  several,  in  the  middle  of  the  focal  interval, 
but  always  nearer  the  anterior  focal  plane,  for  the  reason  that 
v  v'  is  under  all  circumstances  shorter  than  h  h'.  Third,  any 
ellipse  anterior  to  the  circle,  on  the  same  account,  is  shorter  than 
any  posterior  ellipse  taken  at  the  same  distance  from  the  pos- 
terior focal  line  as  the  anterior  is  from  the  anterior  focal  line. 

It  follows  also,  from  the  same  reasoning,  that  the  circles  of 
diffusion  are  greater  on  the  posterior  than  on  the  anterior  focal 
plane. 

§  20.   It  is  abundantly  apparent  from  these  demonstrations  that 


CYLINDRICAL    LENSES. 


it  is  impossible  to  have,  by  any  such  refracting  surface,  a  clearly 
defined  image  of  all  parts  of  an  object  on  any  one  focal  plane.  It 
is  also  evident  that  the  degree  of  astigmatism,  or  the  amount  of 
deviation  from  a  spherical  refraction,  is  measured  by  the  length 
of  the  focal  interval,  that  is,  by  the  difference  in  the  focus  of  the 
meridians  of  greatest  and  least  refraction. 

Fig-  14- 


\ 


FORMATION  OF  A  CYLINDRICAL  LENS. 

§  21.  From  the  foregoing  it  is  seen  that  ordinary  spherical 
lenses  would  have  no  effect  in  correcting  the  astigmatic  condi- 
tion. To  remedy  the  defect  in  form  we  need  lenses  which  are 
curved  only  in  one  direction.  Such  lenses  are  found  in  sections 
of  cylinders  made  in  the  direction  of  their  principal  axes. 

In  the  cylinder  A,  Fig.  14,  e/is  the  axis,  ano*«  b  c  d  a  sec- 
tion made  parallel  to  it.  In  this  section  one  surface  is  plane, 
and  the  other  curved,  but  tlic  curvature  is  only  in  one  direction 
and  that  at  right  angles  to  the  axis. 

The  action  of  such  a  lens  on  an  incident  bundle  of  rays  is 
shown  in  Fig.  15.  The  axis  of  the  cylinder  is/,  and  the  paral- 
lel rays  a  a'  ,*  c',  e  e',  etc.,  falling  in  planes  perpendicular  to 
the  axis  will  be  united,  after  refraction,  in  the  same  planes  at 


REFRACTION    BY    CYLINDERS. 


the  points  a",  c" ,  e",  etc.,  on  the  line  F  F ',  parallel  to  the  axis 
of  the  cylinder/".  Those  parallel  rays  falling  in  planes  parallel 
to /"will  remain  parallel  after  their  passage  through  the  lens. 


REFRACTION  BY  A  CYLINDRICAL  LENS. 
Fig.  16. 

6 


A  CONCAVE  CYLINDER — c  /its  axis. 

§  22.  The  curved  surface  of  the  cylinder  may  be  either  con- 
vex, as  in  Fig.  14,  or  concave,  as  in  Fig.  16;  and  as  the  radius 
of  curvature  may  be  of  any  length,  cylindrical  lenses  may  be 


32  DIFFERENT    FORMS    OF    CYLINDERS. 

made  of  any  refracting  power.     They  are  numbered  according 
to  the  same  system  as  spherical  lenses,  (§  9). 

§  23.  As  in  the  case  of  lenses  with  spherical  surfaces  there 
may  be  several  forms  of  cylinders.  When  one  surface  is  plane 
it  is  called  a  plano-convex  or  plano-concave  cylinder;  when  both 
surfaces  are  curved  after  the  same  manner  it  is  called  double 
convex  or  double  concave.  These  latter  forms,  however,  are  seldom 
used.  When  one  surface  is  cylindrical  and  the  other  spherical 
the  combination  is  called  sphero-cylindrical,  and  when  both  sur- 
faces are  cylindrical,  with  their  axes  at  right  angles  to  each 
other,  they  are  called  crossed  cylinders. 

When  two  plano-convex  or  concave  cylinders  having  the 
same  radius  of  curvature  are  placed  with  their  axes  at  right 
angles  to  each  other  the  refracting  effect  will  be  that  of  a  piano 
convex  or  piano  concave  spherical  lens,  its  focal  distance 
being  that  of  the  cylinders  separately.  Thus  two  -\-2  cys.  with 
their  axes  at  right  angles  would  make  a  -f2  spherical. 

When  the  opposite  side  of  the  cylinder  is  curved  it  is  not 
necessarily  after  the  manner  of  its  own  curvature.  Thus  the 
opposing  surface  of  a  plus  cylinder  may  have  a  concave  spher- 
ical curvature  or  a  concave  cylindrical  curvature  with  its  axis  at 
right  angles  to  the  axis  of  the  positive  lens. 

§  24.  There  is  frequently  a  practical  advantage  to  be  derived  from 
certain  "  over  correcting  "  combinations,  and  it  is  possible  by 
this  means  to  do  away  entirely  with  "  crossed  cylinders,"  which 
are  more  difficult  of  manufacture  than  sphero-cylinders. 

Let  us  suppose,  for  example,  that  we  wish  to  use  a  -f-2  D  cy. 
with  a  — 4  D  cy.,  with  their  axes  at  right  angles.  Instead  of  hav- 
ing one  surface  ground  cylindrically  convex,  of  the  required 
strength,  and  the  other  concavely  so,  with  their  axes  at  right 
angles,  we  can  have  the  following  combination  :  —4  spherical 
on  one  side  and  +6  cylindrical  on  the  other  side.  This  union 
would  leave  the  —4  undisturbed  in  the  meridian  parallel  to  the 
axis  of  the  cylinder,  while  in  the  meridian  at  right  angles  to  it 
the  -f  6  would  neutralize  the  minus  refraction  of  the  4  D  spher- 
ical lens  and  still  leave  a  positive  cylindrical  refraction  of  2  D. 

§  25.     When  two  plane  cylinders  of  opposite    refraction    are 


DENNETT  S    MODIFICATION    OF    STOKES     LENS.  33 

placed  with  their  plane  surfaces  together,  and  revolved  about 
their  common  center  the  result  of  the  combination  is  a  constant 
variation  in  refracting  power,  and  in  the  direction  of  the  axis 
of  the  astigmatic  system.  On  this  principal  Stokes  constructed 
in  1849,  the  lens  which  is  still  known  by  his  name,  though  there 
have  been  modifications  made  in  its  mechanism  by  Javal,  Snel- 
len,  Dennett  and  others. 

If  a  plane  — 3  cy.  and  a  plane  +3  cy.  are  so  placed  that  their 
axes  correspond,  the  one  lens  will  neutralize  the  other.  When, 
however,  they  are  turned  about  their  centers  so  that  their  axes 
are  at  angles,  the  astigmatic  action  will  increase  and  the  axis  of 
the  combined  system  will  change  until  the  axes  of  the  two 
lenses  are  perpendicular  to  each  other,  when  the  total  astigma- 
tion  will  be  equal  to  the  sum  of  the  power  of  the  two  lenses, 
that  is,  6  D.  It  was  hoped  at  one  time  that  this  apparatus,  on 
account  of  its  compactness  and  the  amount  of  astigmatic  action 
it  was  capable  of  representing,  might  come  into  general  use  in 
practical  ophthalmology.  But  the  combination  gives  not  only 
a  cylindrical  action,  but  also  what  amounts  to  a  spherical  re- 
fraction, which  constantly  varies  with  the  rotation,  and  must 
always  be  taken  into  account  when  examinations  are  made,  as 
they  usually  are,  with  parallel  rays. 

Dennett,  of  New  York,  has  recently  made  a  very  in- 
genious modification  of  the  Stokes  lens  by  which  it  is 
possible  not  only  to  vary  the  strength  of  the  cylinders, 
the  axes  remaining  the  same,  but  by  turning  the  same 
milled  head  on  another  set  of  cogs  to  vary  the  direction 
of  the  axes.  Both  the  strength  of  the  cylinders  and  the  direc- 
tion of  their  axes  are  read  off  on  the  apparatus.  The  whole  in- 
strument is  conveniently  mounted  so  that  it  can  be  manipulated 
by  the  patient,  and  for  intelligent  persons  is  most  useful  for  self 
experimentation.  It  is,  of  course,  open  to  the  objection  inher- 
ent in  all  crossed  cylinders  of  the  description  mentioned  above. 
For  examination  at  short  range,  however,  it  may  prove  valuable 
in  speedily  obtaining  the  direction  of  the  principal  meridians, 
and  the  character  and,  approximately,  the  degree  of  astigma- 
tism. 


34 


CYLINDRICAL    ACTION    OF    SPHERICAL    LKNSKS. 


But  a  cylindric  or  astigmatic  action  is  also  obtained  when 
a  spherical  lens  is  placed  obliquely  to  the  path  of  the  rays 
of  light.  In  fact,  the  astigmatism  of  the  eye  was  first  referred 
wholly  to  the  oblique  position  of  the  crystalline  lens  by  Young, 
who  was  the  discoverer  of  ocular  astigmatism.  This  cylindri- 
cal refraction  increases  with  the  degree  of  inclination  of  the  lens. 

The  amount  of  this  cylindrical  action  has  been  computed  by 
Pickering  and  Williams,  and  we  give  in  Table  II  two  of  their  ta- 
bles. One  of  these  represents  the  shortening  of  the  focus  of  a  lens 
of  ico  inches  focal  distance  for  every  five  degrees  of  inclination 
on  the  horizontal  axis.  The  other  shows  the  same  when  the  lens 
is  rotated  on  its  vertical  axis.  These  authors  explain  the  discrep- 
ancy in  the  two  tables  by  the  fact  that  in  the  vertical  inclination 
the  rays  are  no  longer  in  the  same  plane. 

TABLE  II. 


Horizontal  Inclination. 


Vertical  Inclination. 


' 


' 


0° 

100 

0° 

100 

5o 

99-9 

5° 

98.9 

10° 

99.2 

10° 

96.1 

15° 

97-7 

15° 

91.2 

20° 

96.1 

20° 

84.8 

25° 

93-7 

25° 

77-0 

30° 

OI.I 

30° 

684 

35 

88.3 

35° 

59-2 

40° 

84-7 

40° 

49.8 

45o 

81.1 

45° 

40.6 

5°o 

77.2 

5°° 

32.0 

>   55 

73-2 

55 

24.0 

60° 

69.0 

60° 

17.1 

65° 

64.7 

65° 

"•3 

7°o 

604 

70° 

7-0 

8$ 

56.3 
52.1 

g 

85° 

48.3 

85° 

04 

90° 

.44-3 

90° 

O.O 

§  26.  The  rotation  of  a  cylinder  on  its  axis  influences  its  refracting 
power.  Dr.  G.  Hay  has  called  attention  to  this1  and  demonstrated 
mathematically  that  the  focus  of  a  cylindrical  lens  is  shortened 

•Trans.  Amer.  Oph.  Soc.,  1875.     • 


CHANGE  IN  REFRACTION  OF  A  CYLINDER  BY  ROTATING  IT.   35 

by  such  a  rotation  about  its  axis.  Dr.  Sous1  dissents  from  this 
view  and  gives  a  mathematical  demonstration  to  the  opposite 
effect,  and  contends  that  the  lens  in  rotating  about  its  optical 
axis  is  not  increased,  but,  on  the  contrary,  diminished  in  its  re- 
fraction. It  is  not  necessary  to  enter  into  a  mathematical  com- 

TABLE  III. 


Obliquity    Observed                         Neutralizes 
in 
Degrees.                                            Glass. 

Obliquity    Observed 
in 
Degrees. 

Neutralizer 
Glass. 

21       1                                                    l; 

32V.I                                       /6° 

52      ) 

53+  ^        -       - 

-Yl8 

54     J 

27     1 

30    \      -                  -v« 

54     ) 

45     J 

55     \ 

-      -Vie 

371/2  }                   -v,' 

39     J 

57     J 
56     1 

-  }     -    -    •    -/. 

58     / 

56     ) 

47     ) 

58     \        -       - 

-     -Yu 

48     [                          -Yso 

59     J 

49     J 

48        \                                                               i; 

59     J 

58     | 
59      \        -        - 
61     j 

-   -v, 

So+1 

50—^               -              -              -              —  1/20 

60     \ 

j  , 

S2V2J 

61      / 

putation  to  demonstrate  the  fact  that  a  cylinder  does  increase 
in  power  by  being  turned  about  its  axis.  The  following  simple 
experiment  is  sufficient  to  establish  it.  If  a +4  cylinder  is  placed 
before  the  eye,  with  its  axis  horizontal,  and  a  series  of  radiating 
lines  (Snellen's  fan)  is  looked  at,  only  the  vertical  line  will  be 
seen  distinctly,  the  horizontal  lines  being  scarcely  visible.  If  a 
— 3  cylinder  is  now  placed  before  this  lens  with  its  axis  coin^ 
ciding  with  that  of  the  plus  cylinder,  the  horizontal  lines  will 
become  more  distinct,  but  remain  much  less  distinct  than  the 

iTraite  d'  optique,  Paris,  1881,  p.  464,  et  seq. 


36  BIBLIOGRAPHY. 

vertical.  There  still  remains  a  cylindrical  action  of  -f  I  D  un- 
corrected.  If  the  — 3  is  now  rotated  on  its  axis,  the  horizontal 
lines  will  increase  in  clearness,  and  when  it  has  an  inclination 
of  nearly  45°  they  will  be  as  clear  and  distinct  as  the  vertical, 
and  the  whole  fan  will  be  even,  showing  that  the  one  lens  has 
wholly  neutralized  the  other;  in  other  words,  a  —3  rotated  45° 
on  its  axis  has  the  refracting  power  of  a  — 4.  We  copy  Table 
III  from  Dr.  Hays'  paper  showing  the  negative  glass  which 
a  — YTO  neutralizes  when  placed  at  various  inclinations. 

BIBLIOGRAPHY. 


Aubert,  Prof.  H. — Phys.  Optik.  Handb.  d.  gesammet.  Augenheilk.  von  Grafe  tu 
Sftmisch.  B.  II.  1876. 

Ayres,  W.  C— Notes  on  the  Focal  Lines  in  Astig.  N.  Y.  Med.  Jr.  XXXIV.  Pp. 
476-483.  1881, 

Burnett,  S.  M. — Refract  in  the  princpl.  meridians  of  a  tri-axial  ellipsoid,  with  re- 
marks on  the  Correct  of  Astig.  by  cylind.  glasses,  and  an  hist  note  on  corneal  astig. 
Arch,  of  Ophth.  XII.  No.  I.  1883. 

Burnett,  S.  M. — The  action  of  cyl.  glasses  in  the  correction  of  reg.  astig.  Amer. 
Jour.  Oph.  Dec.  1885.  P.  275. 

Dennett,  W.  S  — A  Stokes'  lens  for  measuring  astigmatism.  Trans.  Amer.  Oph. 
Soc.  1885.  P.  106. 

Haltenhoff,  G. — Apparat  z.  optisch.  Demonstrat.  Klin.  Monatsbl.  f.  Augenhlk. 
B.XII.,p.  198. 

Harlan,  G.  C. — Description  of  I.  L.  Borsch's  sph.  cyl.  combination  lens,  ground 
on  one  surface  only.  Trans.  Amer.  Oph.  Soc.  1885.  P.  96. 

Hay,  G. — On  the  increase  of  refract  power  of  a  plano-cylind.  lens  when  rotated 
about  its  axis.  Trans.  Amer.  Ophth.  Soc.,  p.  319.  1875. 

Hay,  G. — On  the  analyt  condit  of  that  form  of  Astig.  pencil  in  which  the  two 
focal  lines  are  perpendicl.  each  to  the  axis  of  the  pencil  and  to  each  other,  and  on 
the  correct  of  such  pencil  by  a  plano-cylind.  lens.  Arch,  of  Ophth.  and  OtoL  N.  Y 
Pp.  497-504.  1876. 

Hay,  G. — Special  applicat  to  the  case  of  the  eye  of  Knapp's  genl.  formulae  for 
astig.  rays.  Arch.  Ophth.  and  OtoL  N.  Y.  II.  No.  I,  pp  79-86.  1871. 

Helmholtz,  H. — Optique  physiologique.  Trad,  par  E.  Javal  et  Th.  Klein.  Paris. 
1867. 

Hoorweg,  J.  L. — Versuch  einer  elemt  Theorie  der  cylind/Linsen.  Arch.  f.  Ophth. 
XIX:  2.  P.  231. 

Kaiser,  H.— Die  Theorie  d.  Astig.  Graefe's  Arch.    B.  XI.    Abt  3,  p.  186.  1865. 

Knapp,  H. — Demonst  of  the  refract  of  light  by  asymmet  surfaces  and  the  deter- 
minat  of  astig.  with  glasses  and  the  Ophthalmoscope.  Trans.  Amer.  Med.  Ass. 
1880. 

Kugel,  C. — Ueber  die  Wirkung  schief  vors  Auge  gestellter  sphar.  Brillengliiser 
beim  regelmassig.  Astig.  Graefe's  Arch.  B.  X.  Abt  I,  p.  89.  1864. 


BIBLIOGRAPHY.  37 

Leroy,  C.  J.  A — Optiq.  physiolog.     Arch.  d'Ophth.     T.  I. 
Leroy — Les  lignes  focales  d.  la  refract  oblique  par  une  sphere   et  la  theorie   de 

Leroy,  C.  J.  A. — Sur  la  theorie  de  1'astig.  Rev.  gen.  d'ophth.  I.  Pp.  429-477.  1882. 

Loomis,  Elias — The  Elements  of  Analyt.  Geometry.     Harper  Bros.     N.  Y.    1873. 

Matthiessen,  Ludwig — Die  Brennlinien  eines  unendlich  diinnen  astigmatischen 
Strahlenbiindels  nach  schiefer  Incidenz  eines  homocentrischen  Strahlenbundels  in 
eine  krumme  Oberflache  und  das  Strahlenconoid  von  Sturm  und  Rummer.  Eine 
Replik.  Grafe's  Archiv.  XXX.  2.  141-154. 

Matthiessen,  L. — Ueber  die  Form  der  Astig,  Bilder  sehr  kleiner  gerader  Linien 
bei  schiefer  Incidienz  der  Strahlen  in  ein  unendlich  kleiner  segment  einer  brechend. 
sphar.  Flache.  Graefe's  Arch.  B.  XXIX.  Abt.  I,  p.  147.  1883. 

Matthiessen,  L. — Grundriss  d.  Dioptrik.     1877. 

Matthiessen,  L. — Ueber  die  Form  eines  unendlich  diinnen  astig.  Strahlenbundels 
und  iiber  die  Kummerschen  Modelle.  Klin.  Monatsbl.  f.  Augenhlk.  XXI,  p.  1013. 
1883. 

Mauthner,  L. — Vorlesung.  iiber  die  opt.     Fehler  des  Auges.     1876. 

Meyer,  H. — Ueber  die  Strahlen  die  ein  leuchtender  Punkt  im  Auge  erzeugt. 
Poggd.  Annal.  B.  XCVII,  p.  233.  B.  XCVIII,  p.  214.  1856. 

Pickering,  E.  C.,  and  Williams,  C.  H. — Foci  of  lenses  placed  obliquely.  Proc. 
Amer.  Acad.  of  Arts.  &  Scs.  N.  S.  Vol.  II.  1874-5. 

Reuss,  v.  A. — Untersuch.  ueber  die  optisch.  ametrop.  Augen.  Graefe's  Arch. 
XXIII,  4.  XXIV,  3. 

Shoen,  Wm. — Beitrage  zur  Dioptrik  des  Auges.     Folio.     Leipsig.     1884. 

Sturm — Memoire  sur  la  theorie  de  la  vision.     Poggd.  Annal.     B.  65.     1845- 

Sturm — Rev.  Gen.  d'oph.     No.  II.     1883. 

Wadsworth,  O.  F. — On  the  effect  of  a  cylind.  lens  with  vertic.  axis  placed  before 
one  eye.  Trans.  Amer.  O^hth.  Soc.  1875. 

Woinow — Ophthalmometrie.     Wien.  W.  Braumiiller.     1871. 


CHAPTER    III. 


ASTIGMATISM    IN    THE    HUMAN    EYE — HISTORY    OF    CORNKAL 

ASTIGMATISM. — THE  DIFFERENT  FORMS  OF  AME- 

TROPIA — VARIETIES  OF  ASTIGMATISM. 

§  27.  The  human  eye,  with  rare  exceptions,  suffers,  among 
other  imperfections,  from  astigmatism.  Even  eyes  that  have  an 
acuteness  of  vision  which  is  normal  according  to  a  convention- 
al standard,  will  be  found,  on  careful  examination,  to  be  astig- 
matic in  a  greater  or  less  degree.  When  this  astigmatism  is 
not  sufficient  to  lower  perceptibly  the  visual  acuteness,  it  is 
considered  normal.  When,  however,  it  is  of  such  a  degree  that 
vision  no  longer  reaches  the  generally  accepted  standard  of 
normality,  it  is  regarded  as  abnormal. 

§  28.  The  refracting  media  of  the  eye  are  the  cornea  and  crys- 
talline lens,  and  astigmatism  may  be  found"in  either  or  both.  In 
addition,  therefore,  to  the  division  into  regular  and  irregular, 
astigmatism  (§  12)  may  be  divided  into  corneal  and  lenticu- 
lar. 

Corneal  astigmatism  is,  for  the  most  part,  regular;  while 
lenticular  astigmatism  is,  most  generally,  irregular.  To  this 
general  rule,  however,  there  are  exceptions,  which  will  be  con- 
sidered when  each  form  is  treated  of  in  detail. 

§  29.  The  cornea  in  normal  eyes  suffers,  in  addition  to  the 
regular  form  of  astigmatism,  in  which  the  opposing  meridians 
have  different  foci,  from  a  monochromatic  aberration  in  these 
meridians  themselves,  which  undoubtedly  exercises  an  influ- 
ence on  the  distinctness  of  the  retinal  image. 

The  outline  of  the  corneal  surface  in  the  optically  normal 
eye  has  never  been  determined  with  exactness,  nor  the  peculi- 
arities of  its  refraction  treated  of  in  a  thorough  manner.  I 
therefore  asked  my  friend  Prof  Wm.  Harkness,  of  the  United- 

(38) 


ASTIGMATISM  OF  THE  HORIZONTAL  CORNEAL  MERIDIAN.         39 

States  Naval  observatory,  to  take  the  data  derived  from  the 
measurements  of  a  number  of  emmetropic  eyes,  and  determine 
what  the  actual  refraction  of  the  normal  cornea  is  in  one  me- 
ridian of  its  curvature. 

This  he  kindly  did,  and  the  results  are  published  in  the  Ar- 
chives  of  Ophthalmology,  vol.  xii.  pp.  9—19.  A  resume  of  his 
investigations  is  herewith  given : 

"  The  cornea  of  the  emmetropic  eye  seems  to  have  an  ellip- 
soidal form,  but  the  existing  data  for  determining  its  curvature 
in  the  vertical  meridian  are  too  meagre  to  give  a  satisfactory 
result.  I  have  therefore  confined  my  attention  to  the  hori- 
zontal meridian,  and  have  taken  the  data  for  it  from  table  VII, 
upon  pages  598—599  of  Mauthner1.  That  table  exhibits  the 
form  and  dimensions  of  the  cornea  in  seventeen  pairs  of  em- 
metropic eyes,  and  from  the  mean  of  these  thirty-four  eyes,  it 
appears  that  in  the  visual  axis  the  radius  of  curvature  is  7.708 
millimetres,  while  20°  to  the  inner  side  of  that  axis  it  is  8.378 
millimetres,  and  20°  to  the  outer  side  7.884  millimetres.  Mauth- 
ner does  not  explain  the  phrase  "  20°  to  the  inner  (or  outer) 
side  of  the  visual  axis,"  and  I  have  had  some  trouble  in  ascer- 
taining its  true  meaning. 

"  It  is  customary  to  regard  the  outline  of  the  cornea,  along  a 
horizontal  section  through  the  visual  axis,  as  part  of  an  ellipse. 
Let  it  be  part  of  the  ellipse  NAME,  Fig.  17,  of  which  the  major 
and  minor  semi-axes  are  respectively  AH  and  BH;  and  let  C,  D, 
E,  be  the  points  at  which  the  radii  of  curvature  are  measured. 
DF,  CF  and  EF  are  normals  to  the  ellipse  at  these  points, 
and  CFis  the  visual  axis.  By  the  phrase  "20°  to  the  inner  side  of 
the  axis"  Mauthner  means  that  the  angle  CFD,  between  the  visual 
axis  and  the  normal  at  D,  is  20°;  and,  similarly,  by  "20°  to  the 
outer  side  of  the  visual  axis"  he  means  that  the  angle  CFE  is 
20°.  It  may  be  well  to  remark  that  Fig.  17  is  accurately 
drawn  to  scale,  and  the  arc  NAM  represents  that  portion  of 
the  ellipse  which  is  included  within  the  limits  of  the  cornea. 
*******  -piie  monochromatic  aberration  of  the 

'Vorlesungen  ii.  d.  optis.,  Fehler  des  Auges,  1876. 


4O         ASTIGMATISM  QF  THE  HORIZONTAL  COKM-AL  MMKIDIAN. 


cornea  is  most  conveniently  investigated  by  tracing  the  paths 
which  a  considerable  number  of  parallel  rays  impinging  upon 
it  will  pursue  within  the  eye.  Eleven  such  Wys  have  been  con- 
sidered, all  situated  in  the  same  horizonta^plane,  at  intervals 

Fig.  77. 


r  SHOWING  THE  ELLIPTICAL  FORM  OF  THE  COR' 
A  H  the  Optical  Axis. 


— C  F  is   the  Visual   Axis; 


of  half  a  millimetre  from  each  other,  and  the  central  one  coin- 
ciding with  the  visual  axis.  For  their  passage  a  pupil  of  five 
millimetres  in  diameter  is  necessary.  The  eleven  rays  in 
question  furnish  eleven  values  of  d,  varying  by  intervals  of  half 
a  millimetre  from  -f  2.5mm  (towards  the  nose),  to  —  2.5"""  to- 
wards the  temple),  from  which  the  corresponding  values  of  F 
have  been  computed." 

The  results  of  these  computations  are  represented  graphic- 
ally in  Fig.  1 8.  The  center  line  o  is  the  visual  axis,  while  — 3, 
2,  I,  represent  the  distance  toward  the  temple  in  millimetres, 
and  -f-3»  2,  i,  the  distance  towards  the  nose  in  millimetres. 
The  ordinates  represent  the  paths  of  the  eleven  rays  whose  foci 
have  been  computed.  The  values  of  Fare  taken  as  abscissas, 


FOCAL  CURVE  OF  THE  NORMAL  CORNEA. 


and  the  curved  line  shows  the  position  of  these  foci  at  intervals 
of  one-tenth  of  a  millimetre.  From  this  it  is  evident  that  the 
focal  curve  is  a  parabola. 


Fig.  18. 


Z 


z 


31.0 


30.5 


30.0 


29.5 


012+3 

Nose  — >• 

SHOWING  THE  FORM  OF  THE  FOCAL  CURVE  OF  THE  NORMAL  CORNEA. 

"Table  IV  shows  how  the  monochromatic  aberration  actually 
existing  in  the  normal  cornea  compares  with  what  would  have 
existed  if  the  cornea  had  been  spherical.  Upon  each  line  of 
the  table,  the  first  column,  d,  contains  the  assumed  diameter  of 
the  pupil ;  the  second,  third  and  fourth  columns  relate  to  the 
normal  cornea,  and  contain  respectively  the  greatest  and  least 
focal  distance  occurring  within  the  area  of  the  pupil,  and  the 
amount  of  astigmatism  corresponding  to  them ;  the  fifth,  sixth, 
and  seventh  columns  relate  to  a  spherical  cornea,  and  contain 
similar  data  for  it.  In  computing  the  focal  distance  at  various 
points  of  a  spherical  cornea  it  has  been  assumed  that  the  radius 
of  curvature  r  =  7.708""",  and  the  index  of  refraction  >j  =1.3366. 

As  the  monochromatic  aberration  we  are  considering  occurs 


42       COMPARISON  OF  THE  NORMAL  AND  A  SPHERICAL  CORNEA. 

TABLE  IV. 


Normal  Cornea. 

Spkerical  Cornea. 

a. 

* 

"• 

At. 

F. 

f 

A*. 

mm. 

I 

mm. 
30.684 

mm. 
30.502 

Par.  in. 
1:139 

mm. 
30.608 

mm. 
30.556 

Par.  in. 
1:476 

2 

3 

4 
5 

a 

.728 
30.728 

•359 
30.182 
29.971 
29.724 

i:  46 

«:  33 
i:  25 

.608 
.608 
.608 
30.608 

30.171 
29.826 
29.376 

I  130 
I     58 

I     32 
I      21 

in  a  single  meridian,  its  correction  by  cylindrical  lenses  is  im- 
practicable, but  nevertheless  its  amount  may  be  expressed  in 
the  notation  usually  employed  for  astigmatism.  The  requisite 
formula  is 

Astigmatism  =  0.0396  (F—F1) 

In  which  F  and  F'  are  the  lengths  in  millimetres  of  the 
greatest  and  least  focal  distances  found  within  the  area  of  the 
pupil,  and  the  result  is  expressed  in  terms  of  the  Paris  inch. 

In  conclusion,  the  results  at  which  we  have  arrived  may  be 
summed  up  as  follows : 

a.  The  monochromatic  aberration  originated  by  the  normal 
cornea  occurs  principally  on  the  outer  side  of  the  visual  axis — 
that  is,  on  the  side  farthest  from  the  nose. 

b.  The  diameter  of  the  pupil  is  usually  about  four  millime- 
tres.    For  diameters  less  than  this,  the  monochromatic  aberra- 
tion of  a  spherical  cornea  would  be  less  than  that  of  the    nor- 
mal cornea.     For  greater  diameters  the  reverse  is  true.     This 
is  contrary  to  the  generally  received  opinion.     (See    Bonders, 
foot-note  on  page  310.) 

f.     Bonders  says  (pp.  456,  457,  Anomalies  of  Ref.  and   Ac- 
corn,  of  the  Eye),  the  astigmatism  in  sharp  eyes  is    not   gener-  r 
ally  more  than  from  1:140  to  1:60,  and  whenever  it  exceeds  the  i 
latter  amount  the  power  of  vision  suffers  under   some    circum-  \ 
stances.     An  astigmatism  of  i  :4O  he  regards  as    decidedly   ab- 
normal.    Nevertheless,  with  a  pupil  four  millimetres  in  Miame- 
ter  the  normal  cornea  produces  monochromatic    aberration   to 
the  extent  of  1:." 


NORMAL  ASTIGMATISM  OF  THE  CORNEA.  43 

Aubert  (Archiv.  f.  d.  gesammt  Phys.  B.  xxxv)  has  recently 
made  some  measurements  in  order  to  determine  more  ac- 
curately the  form  of  the  corneal  surface,  and  has  found  that  at 
about  12°  towards  either  side  of  the  visual  axis  it  becomes 
very  rapidly  flattened,  thus  dividing  the  stirface  into  two  true 
zones,  the  polar  and  peripheral.  The  central  or  polar  zone, 
which  is  used  exclusively  for  optical  purposes,  he  calls  the  op- 
tical zone ;  the  peripheral,  bordering  on  the  sclera,  he  calls  the 
scleral  zone.  The  regular  curve  of  the  optical  zone  reaches 
about  17°  to  either  side  of  the  apex  of  the  cornea,  but  even  in 
a  very  wide  pupil  the  rays  refracted  through  the  scleral  zone 
cannot  enter  the  eye.  In  these  measurements  he  has  not  de- 
termined the  question  of  whether  the  optical  zone  is  spherical 
or  elliptical. 

§  30.  But  aside  from  this  monochromatic  aberration  of  the 
cornea  in  a  single  meridian  (which  must  be  considered  as 
forming  a  part  of  its  irregular  astigmatism)  there  exists,  in 
most  eyes,  a  difference  in  the  curvature  of  the  principal  merid- 
ians taken  as  a  whole,  constituting  regular  astigmatism. 

A  number  of  eyes  with  normal  vision  have  been  measured 
as  to  the  curvature  of  their  various  corneal  meridians,  and  in 
almost  all  there  has  been  found  a  meridian  of  least  curvature 
(longest  radius),  and  at  right  angles  to  this  another  of  greatest 
curvature  (shortest  radius).  In  other  words,  the  human  cornea 
does  not  represent,  by  its  surface,  the  section  of  a  sphere  with 
equal  radii,  but  approaches  in  form  more  nearly  to  an  ellipsoid 
with  three  unequal  axes,  such  as  we  have  studied  in  Chapter 
II. 

In  the  table  V  are  given  the  results  of  measurements 
of  twenty-one  normal  eyes,  showing  the  amount  of  astigmatism 
from  which  they  suffer. 

It  will  be  seen  from  an  examination  of  this  table  that 
in  only  two  eyes  were  the  two  principal  corneal  meridians  the 
same.  In  the  other  nineteen  there  was  a  difference,  esti- 
mated'by  the  focal  distance  of  the  lens  necessary  to  correct  it, 
and  expressing  the  amount  of  the  astigmatism,  of  from  1:280  to 
1:38- 


44 


NORMAL  ASTIGMATISM  OF  THE  CORNEA. 

TABLE  V. 


No. 

Observer. 

AW/Vr  in 
Horizontal 
Meridian. 

Radius  in 
I  'ertical 
Meridian. 

Focnt  in 
Horizontal 
Meridian. 

Focus  in 
Vertical 
Meridian. 

Astigtnation 
=  i: 

I 

2 

d 

Mm. 
7.80 

8.07 

Mm. 
7.91 
8.26 

Paris  Inches. 
I.I445 

Paris  Inches. 
.1605 
.2120 

Paris  Inches 
—62 
—40 

3 

0. 

7-23 

7.385 

1.  0688 

.0835 

-38 

4 

c 

7.22 

7.08 

1-0593 

.0388 

40 

5 

774 

7.71 

1.1356 

-'3'3 

220 

6 
7 

7-74 

8.20 

7-74 

8.12 

'•1356 
I.203I 

•1356 
.1914 

88 

B 

8-34 

8.19 

1.2237 

.2107 

85 

9 
10 
ii 

i 

7-23 
8.27 
7-73 

7-23 
8.30 
769 

1.  0608 
I.2I34 
I.I342 

.0608 
.2178 
.1283 

"tg 

12 

'3 

•c 
c 

8.15 

7-94 
78i 

1.1958 
1.1855 

.1650 
•*457 

34 
29 

14 

e« 

(A 

8.02 

7-92 

1.1767 

.1626 

76 

15 

7-42 

7-30 

10887 

.0711 

5° 

1  6 

•o 

749 

1.0987 

.1019 

—280 

17 

o 

749 

745 

1.0987 

-093' 

1  60 

a 

C 

7-84 

746 

1.1503 

.0946 

16.9 

19 

7-75 

7-33 

1.1371 

•0755 

14.9 

20 

7.60 

I.II5J 

.1048 

89 

21 

7-55 

7.60 

I.I078 

.1151 

—127 

It  should  be  stated  in  this  connection,  however,  that  the  cor- 
neal  astigmatism  does  not  in  all  cases  represent  the  exact  as- 
tigmatism from  which  the  eye  suffers.  There  may  be  a  concomi-  ^ 
tant  lenticular  astigmatism  which  will  increase  or  diminish  that 
of  the  cornea  according  to  the  direction  of  its  faulty  meridian 
and  the  degree  of  its  astigmatic  deviation.  The  total  astigma- 
tism of  the  eye  is  the  algebraic  sum  of  its  corneal  and  lenticu- 
lar astigmatism.  This  we  shall  deal  with  further  on  under  the 
head  of  lenticular  astigmatism. 

It  will  be  furthermore  observed  that  in  thirteen  cases  the 
vertical  was  the  more  strongly  curved  meridian,  the  horizontal 
being  the  stronger  in  only  six  cases  (those  marked  —  in  the 
table).  Clinical  observation  being  in  accord  with  this,  it  is  cus- 
tomary to  speak  of  this  relation  of  the  principal  meridians  in 
which  the  vertical  is  the  more  strongly  curved  as  being  accord- 
ing to  the  rule. 

§31.  The  existence  of  a  slight  degree  of  astigmatism  in  a  normal 


REGULAR    LENTICULAR  ASTIGMATISM.  45 

eye  can  be  experimentally  demonstrated  by  turning  before  it  a 
weak  cylindrical  glass — say,  with  a  focal  distance,  positive  or 
negative,  of  144  inches  (0.25  D).  In  this  experiment  it  will  be 
found  that  when  the  axis  of  the  cylinder  corresponds  to  one 
certain  meridian  vision  will  be  best,  and  when  it  corresponds  to 
the  one  at  right  angles  to  it  it  is  worst.  In  the  first  instance 
the  cylinder  corrects  the  existing  astigmatism,  and,  perhaps 
slightly  over  corrects  it,  while  in  the  latter  it  increases  it  by  the 
power  of  the  lens. 

If  two  very  fine  threads  are  crossed  at  right  angles  and 
brought  gradually  towards  the  nearest  point  of  distinct  vision, 
it  will  be  found,  usually,  that  one  becomes  blurred  before  the 
other.  The  point  where  the  first  thread  becomes  indistinct 
marks  the  near  point  of  the  weakest-refracting  meridian,  the 
point  where  the  line  at  right  angles  to  it  becomes  blurred  is 
the  near-point  of  the  most  strongly  refracting  meridian.  The 
difference  between  the  two  points  measures  the  amount  of  as- 
tigmatism. This  is  the  method  used  by  Young  in  demonstrat- 
ing his  astigmatism. 

§  32.  Regular  astigmatism  may  also  have  its  seat  in  the  lens. 
Thomas  Young,  who  was  the  first  to  demonstrate  the  existence 
of  astigmatism  in  the  human  eye,  found  his  own  astigmatism  to 
reside  there.  He  immersed  his  eye  in  a  chamber  of  water 
bounded  by  a  plane  glass  surface,  thus  eliminating  the  refrac- 
tion of  the  cornea,  and,  as  the  difference  in  the  refraction  of 
the  two  meridians  did  not  disappear,  he  rightly  concluded  that 
it  must  be  due  to  an  abnormality  of  the  lens. 

The  causes  of  lenticular  astigmatism  are  either  displacement 
of  the  lens  in  such  a  manner  that  its  refracting  surfaces  shall 
lie  obliquely  to  the  visual  axis  (§  25),  or  a  difference  in 
curvature  of  its  principal  meridians,  as  in  corneal  astigmatism. 
Young  conceived  his  astigmatism  to  be  due  to  an  obliquity  of 
the  lens. 

A  simple  displacement  of  the  lens  at  right  angles  to  the 
visual  axis  would  not  of  itself  produce  astigmatism. 

There  have  been  some  cases  reported  of  progressive  change 
in  the  degree  of  astigmatism  and  in  the  direction  of  the  prin- 


46  HISTORY  OF  CORNEAL  ASTIGMATISM. 

cipal  meridians.  In  none  has  there  been  any  measurement  of 
the  corneal  radius,  and  under  these  circumstances  we  cannot 
positively  exclude  a  change  in  corneal  curvature,  but  it  is  most 
probable  that  the  change  is  due  to  alteration  in  the  shape  of 
the  lens,  either  from  changes  in  its  substance  or  from  a  modi- 
fied action  of  the  ciliary  muscle. 

§33.  It  is  probable  that  Gerson  (1810)  was  the  first  to  point  out 
the  existence  of  corneal  astigmatism,  but  I  do  not  find  that  the 
opinion  was  based  on  ophthalmometric  measurements,  and  his 
statement  only  became  generally  known  after  the  fact  had  been 
established  by  the  measurements  of  others.  Wilde  and  Jones 
refer  to  ''cylindrical  eyes"  and  "cylindrical  cornea,"  but  there  are 
no  evidences  that  these  opinions  were  based  on  opthalmometric 
measurements. 

Wilde  says1:  "  It  is  well  known  that  the  cornea  is  not  a  cor- 
rect surface  of  revolution,  but  that  the  curvature  of  its  hori- 
zontal plane  is  less  than  that  of  its  vertical.  When  this  ex- 
ceeds the  normal  extent  it  gives  rise  to  irregular  refraction, 
causing  a  circle  to  appear  oval." 

Jones  simply  quotes  from  the  history  of  Airy's  case.  No 
practical  application  of  these  facts  seems  to  have  been  made 
by  either  of  these  writers. 

Senf  was  the  first  (in  1846)  to  make  measurements  of  the 
cornea,  which  showed  it  to  be  ellipsoidal  rather  than  spherical 
in  shape.  Helmholtz  arrived  at  the  same  conclusion  from  his 
ophthalmometrical  measurements  which  were  published  in 
Grafts  Archives  B.  i,  Abt.  2  (1855).  In  this  article  (p.  18)  he 
says :  "  The  form  of  the  cornea  corresponds  approximately  to 
an  ellipsoid  formed  by  the  revolution  of  an  ellipse  about  its 
major  axis." 

He  gives  these  measurements  as  well  as  those  of  Senf  in  the 
first  part  of  his  "  Physiologische  Optik  "  (pages  8  and  1 1  of 
the  French  edition),  published  in  1856;  but  it  is  evident  that 
he  still  considered  the  cornea  to  be  an  ellipsoid  of  revolution, 
as  his  measurements  were  confined  to  one  meridian  (the  hori- 

1  Dub.  Jn'l  Med.  Sci.     1846-47.     P.  105. 


HISTORY  OF  CORNEAL  ASTIGMATISM.  4/ 

zontal).  He  speaks  at  this  time  (p.  142)  of  the  astigmatism  of 
Young  as  being  caused  by  the  lens,  and  of  the  correction  of 
his  own  astigmatism  (of  low  degree)  by  means  of  an  obliquely 
placed  concave  lens,  but  no  hint  is  given  that  the  cause  of  the 
astigmation  was  in  the  cornea. 

It  was  Knapp  who  first  determined  by  ophthalmometric 
means  that  the  cornea  was  not  an  ellipsoid  of  revolution  but 
an  ellipsoid  with  three  unequal  axes. 

In  the  "Verhandlungen  der  vom  3-6  Sept.,  1859,  *m  Heidelberg 
versammelten  Augen  JErtze,"  Berlin,  Peters,  1860,  we  find  (p. 
19)  that  "Dr.  Knapp  gave  an  account  of  his  measurements  on 
the  curved  surface  of  the  human  eye,  made  by  means  of  Helm- 
holtz's  ophthalmometer.  i.  The  cornea.  Helmholtz's  meas- 
urements were  confined  to  the  horizontal  meridian.  Knapp,  on 
the  other  hand,  had  measured  four  eyes  in  many  different 
meridians  with  the  following  result :  I.  The  centre  and  apex 
of  the  cornea  do  not  coincide.  *  *  *  The  anterior  focal 
distance  of  the  horizontal  ellipse  =23.095  mm.\  of  the  vertical 
ellipse  =23.34  mm.  The  posterior  focal  distance  of  the  hor- 
izontal ellipse  =30. 1 8  mm.\  of  the  vertical  ellipse  =31.1  mm. 
*  *  *  In  the  discussion  on  this  division  of  the  subject, 
Knapp  remarked  that  in  all  probability  it  was  the  difference 
between  the  vertical  and  horizontal  ellipses  which  rendered 
cylindrical  glasses  necessary,  and  was  the  cause  of  the  differ- 
ence in  the  '  accommodation  line '  in  the  vertical  and  horizon- 
tal directions.  After  cataract-extraction,  in  sclerectasia  and 
hyperpresbyopia,  such  glasses  were  of  benefit,  as  had  been 
shown  by  Prof.  Bonders. 

"  In  regard  to  the  accommodation-line,  Prof.  Bonders  re- 
marked that,  in  his  opinion,  it  was  due  to  the  lens,  from  the 
fact  that  it  was  in  intimate  connection  with  polyopia,  which 
was  undoubtedly  caused  by  the  lens,  as  proven  by  entopic  ex- 
periments." 

These  investigations  were  published  in  detail  by  Knapp  in 
his  inaugural  thesis,  "  Bie  Krummung  der  Hornhaut  des 
menschlichen  Auges  "  in  1860. 

Bonders,  in  his  first  papers  on  the  refraction  and  accommo- 


48  HISTORY  OF  CORNEAL  ASTIGMATISM. 

dation  of  the  eye,  published  in  Graffs  Archives,  makes  in 
B.  vii,  Abt.  I,  p.  176  (1860),  an  application  of  this  asymmetry 
to  the  explanation  of  abnormal  astigmatism,  in  contradis- 
tinction to  the  lenticular  theory  of  Young,  and  gives  reference 
to  Knapp's  paper.  So  far  as  I  know  this  is  the  first  mention 
made  by  Bonders  of  corneal  astigmatism.  In  Grafe's  Archives 
B.  viii,  Abt.  2  (1862),  appeared  Knapp's  classical  paper,  "Ueber 
die  Assymmetrie  des  Auges  in  seinen  verscheidenen  Meridi- 
anebenen."  While  this  paper  was  in  press  Donders  published 
his  "  Astigmatisme  en  cylindrische  Glazen,"  which,  for  the 
first  time,  brought  the  subject  of  astigmatism  and  its  cor- 
rection prominently  before  the  profession.  Soon  afterward 
(1864),  his  treatise  on  the  "Anomalies  of  the.  Refraction  and 
Accommodation  of  the  Eye  "  appeared,  which  made  astigma- 
tism a  part  of  the  general  knowledge  of  the  profession. 

The  opinion  that  regular  astigmatism  resides  almost  wholly 
in  the  cornea  has  been  most  thoroughly  substantiated  by  all 
observations  made  since  that  time.  Javal  in  the  Annales  d' 
oculistique,  t.  87,  pp.  33-43  (1882),  says  that  in  the  testing  and 
measurement  of  more  than  100  eyes,  the  total  astigmatism 
corresponded  exactly  with  the  corneal  astigmatism,  with  the 
exception  of  four  cases,  and  in  one  of  these  the  difference  was 
only  O.2  D ;  and  additional  examinations  by  him,  and  by  Dr. 
Nordenson,  amounting  to  more  than  250  cases,  have  confirmed 
his  first  observations. 

My  own  experience  with  Javal's  ophthalmometer  tends  to 
substantiate  this  opinion  in  the  main,  though  my  percentage  of 
difference  between  the  total  and  corneal  astigmatism  is  greater 
than  that  given  by  Javal  and  Nordenson. 

§  34.  As  stated  in  §  27,  when  the  astigmatism  reaches  such 
a  degree  as  to  reduce  the  visual  acuteness  below  the  normal 
standard  of  */4  (M/M)  it  is  called  abnormal. 

Exactly  what  degree  of  astigmatism  should  be  considered 
abnormal  has  not  been  agreed  upon  by  observers.  Some  look 
upon  '/i»  (0.25  D)  as  abnormal,  while  others  think  1/1,  (0.50) 
normal.  It  is  impossible  to  formulate  any  law  of  universal  ap- 
plication for  such  a  varying  and  imperfect  optical  instrument 


THE    EMMETROPIC    EYE. 


49 


as  the  eye.  Prof.  Harkness  has  shown  us  (§  29)  that  the  nor- 
mal irregular  astigmatism  of  a  single  meridian  does  not  proba- 
bly fall  below  l/S3,  and  since  a  large  majority  of  persons  cannot 
distinguish  any  sensible  difference  in  the  distinctness  of  the 
image  of  test  objects  as  fine  as  the  finest  test-types  when  a 
correcting  0.25  is  placed  before  their  eye  with  its  curvature 
corresponding  to  the  faulty  meridian,  we  fee/  justified  in  con- 
sidering only  those  degrees  of  astigmatism  abnormal  which  ex- 
ceed 0.25  (Vino)-  We  would,  however,  not  deny  the  possi- 
bility of  certain  rare  cases  deriving  benefit  from  the  employment 
of  glasses  of  this  low  power. 

§35.  When  we  come  to  study  astigmatism  as  it  affects  the 
human  eye  in  detail,  we  find  that  we  have  several  different  con- 
ditions to  deal  with,  and  in  order  to  clearly  understand  the 
manner  and  degree  of  departure  of  the  astigmatic  from  the 
optically  normal  eye  we  must  know  in  what  the  latter  consists. 

§  36.  A  normal,  standard  or  emmetropic  eye  (that  is,  an  eye 
of  proper  measure)  is  one  whose  retina  lies  at  the  focus  of  its 
refracting  media. 

Fig.  19. 


THE  EMMETROPIC  AND  AMETROPIC   EYES  COMPARED — ff,  the  hypermetropic  ; 
E,  the  emmetropic ;  M,  the  myopic  eye. 

Parallel  rays  falling  on  all  meridians  of  such  an  eye  are 
brought  to  a  focus  at  the  same  point  on  the  retina,  E,  Fig.  19. 

§  37.  An  eye  which  deviates  from  these  standard  refractive 
conditions  is  called  ametropic  (not  of  proper  measure). 


50  MYOPIA    AND    HYPERMETROPIA. 

When  the  parallel  rays  are  focussed  before  the  retina,  Mt  Fig. 
19,  the  eye  is  called  myopic.  When  they  cross  behind  the  reti- 
na situated  at  //,  the  eye  is  said  to  be  hypermetropic. 

§  38.  In  the  ordinary  myopic  and  hypermetropic  forms  of 
ametropia  it  has  been  found  from  ophthalmometric  measure- 
ments, that,  as  a  rule,  the  radius  of  curvature  of  the  cornea  is 
the  same  for  them  as  for  the  emmetropic  eye.  These  ame- 
tropic  conditions  are  due,  except  in  rare  cases,  to  a  displace- 
ment of  the  retina ;  in  other  words,  to  a  variation  in  the  length 
of  the  eyeball.  A  myopic  eye  is  one  that  is  too  long ;  a  Jiyper-^ 
me  tropic  eye  is  one  that  is  too  short.  Ordinary  myopia  and  hy- 
permetropia  are,  therefore,  not  strictly  speaking  anomalies  of 
refraction,  since  the  refracting  power  of  these  eyes  is  normal 
as  compared  with  that  of  the  .emmetropic  eye.  The  refraction 
is  abnormal  only  when  considered  in  reference  to  the  position 
of  the  retina. 

In  those  exceptional  instances  where  the  refraction  is  at 
fault  its  seat  may  be  in  the  cornea  or  the  lens.  ' 

§  39.  Astigmatism  is  the  only  anomaly  which  is  due  en- 
tirely to  a  defect  in  the  refracting  apparatus,  for,  as  we 
have  seen,  it  is  the  faulty  curvature  of  the  refracting  media 
which  is  the  cause  of  the  optical  error. 

§  40.  We  can  now  understand  how  astigmatism,  in  addition 
to  its  own  error  in  ^refraction,  may  be  complicated  with  the 
other  forms  of  ametropia. 

The  foci  of  both  meridians  may  lie  in  front  of  the  retina,  as 
in  myopia,  or  they  may  lie  behind  it,  as  in  hypermetropia,  <>r 
one  may  be  in  front  and  the  other  behind  it,  constituting  my- 
opia and  hypermetropia  at  once. 

It  is,  therefore,  important  not  only  to  facilitate  study,  but,  as 
we  shall  see,  for  the  practical  purpose  of  correcting  the 
anomaly,  that  we  make  subdivisions  of  astigmatism.  The  gen- 
eral forms  into  which  it  has  been  divided  are  :  I.  The  simple. 
2.  The  compound.  3.  The  mixed. 

§41.  SIMPLE  ASTIGMATISM.  When  the  focus  of  one  merid- 
ian falls  on  the  retina  the  astigmatism  is  called  simple.  There 
can,  of  course,  be  but  two  varieties  of  this  form,  one  in  which 


THE    DIFFERENT    FORMS    OF    ASTIGMATISM.  51 

the  focus  of  the  faulty  meridian  falls  in  front  of  the  retina,  and 
the  other  in  which  it  falls  behind  it.  Borrowing  the  nomencla- 
ture of  spherical  ametropia,  the  first  condition  is  called  simple 
myopic  astigmatism,  and  the  second,  simple  hypermetropic  as- 
tigmatism. One  meridian  is  emmetropic,  the  other  myopic  or 
hypermetropic. 

§  42.     COMPOUND   ASTIGMATISM.      In   the    compound   form  l> 
both  foci  fall  either  in  front  of  or  behind  the   retina.     When  A. 
the  foci  lie  before  the  retina  it  is  called  compound  myopic  astig- 
matism ;  when  they  both  lie  behind  it  there  is  compound  hyper- 
metropic astigmatism.     In  this  form,  therefore,  we  have  an  as- 
tigmatism associated  with  spherical  ametropia.     Both  meridi- 
ans are  ametropic,  and  in  the  same  manner,  but  one  of  greater 
degree  than  the  other. 

§  43.     MIXED  ASTIGMATISM.     This   is  the  condition   where V, 
the  focus  of  one  meridian  lies  in  front  of  and  the  other  behind!  \ 
the  retina.     In  other  words,   one   meridian  is  myopic  and  the 
other  hypermetropic.     Of  this  form  there  can  of  course  be  but 
one  variety. 

Every  case  of  regular  astigmatism  must  be  of  one  of  these 
three  forms. 

BIBLIOGRAPHY. 


Airy,  George  Biddell — On  a  peculiar  defect  in  the  eye,  and  a  mode  of  correcting 
it.     Trans.  Camb.  Philos.  Soc.     V.  2.     1827.     P.  267-271.     (Read  Feb.  21,  1825). 

Airy,  G.  B. — On  a  change  in  the  state  of  an  eye  with  a  malformation.     Trans. 
Camb.  Philos.  Soc.    V.  8.     1849.     P.  361-362.     (Read  May  25,  1846). 

Arago— Oeuv.  Complt.    T.  XI.     P.  218.     1844. 

Aubert,  H. — Phys.  Optik.,  Handb.  d.  gesammt.  Augenheilk  von  Grafe  u.  Samisch. 
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Aubert,  H. — Naehert  sich  die  Hornhautkriimmung  am  meisten  der  Ellipse.    Arch. 
f.  d.  gesam.  Physiol.     Bonn.     B.  XXXV.     P.  587.  1885. 

Bergeron,  G. — Astig.     N.  diet,  de  med.  et  de  chir.  prat.     Pp.  740-9.    1865. 

Briicke,  E. — Ueber  asymmet    Strahlenbrech.  im   mensch.   Auge.     Sitzbr.   d.   K 
Akd.d.  Wisschft.     1868. 

Buckner,  J.  H. — Astig.     Cincin.  Lancet  and  Obs.     XVIII.     Pp.  466-80.     1875. 

Bumstead,  F.  J. — A    few   Rem.   on   Astig.    Am.  Med.  Times.     New  York.     VII 
Pp.  203-5.  1863. 

Burnett,  S.  M. — Character  of  the  foe.  lines  in  astig.     Arch,  of  Ophth.  New  York 
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52  BIBLIOGRAPHY. 

Burnett,  S.  M. — Refract  in  the  prihcip.  merid.  of  a  triax.  ellipsoid,  etc.  Arch,  of 
Ophth.  XII.  No.  i.  1883. 

Carter,  R.  B. — On  defects  of  vision.     London.     1877. 

Cohn,  Hermann — Untersuch.  der  Aug.  v.  10060    Schulkindern.      Leipzig.     1867. 

Donders,  F.  C. — Astigmatism  in  cylindrische  glazen.     Utrecht.     1862. 

Donders,  F.  C. — Der  Sitz  des  Astig.  (nach  Middleburg)  u.  d.  Excursion  der  Beweg. 
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Donders,  F.  C. — BeitrSg  z.  Kenntniss  der  Refract,  u.  Accommodat.  Anomal. 
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374-9.S58-6'-     '853- 

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1848. 

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BIBLIOGRAPHY.  53 

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CHAPTER  IV. 


DIAGNOSIS    OF   ASTIGMATISM — DETERMINATION    OF    ITS    FORM 

AND  DEGREE,  AND  THE  DIRECTION  OF  THE 

PRINCIPAL  MERIDIANS. 

§  44.  When  a  case  of  supposed  astigmatism  presents  itself 
for  examination  there  are  four  points  to  be  settled  :  a,  whether 
any  astigmatism  exists ;  b,  if  it  does,  the  direction  of  the  prin- 
cipal meridians ;  c,  the  special  form  of  the  anomaly,  and  d,  its 
degree. 

§  45.  For  simplicity  of  illustration  we  will  assume  that  in 
the  case  under  consideration  there  does  not  exist  any  turbidity 
of  the  refracting  media,  any  affection  of  the  nervous  appara- 
tus, or  any  of  the  complications  which  we  shall  consider  in 
detail  later  on,  but  will  regard  it  as  a  purely  optical  difficulty. 

§  46.  In  order  to  determine  the  first  point,  we  place  the  pa- 
tient, as  we  always  do  when  examining  the  static  refraction  of 
an  eye,  at  a  distance  of  15  or  20  feet  (4  to  6  metres)  from  the 
well-known  test  types  of  Snellen.  The  acuteness  of  vision  of 
each  eye  is  then  taken  separately ;  and  if  we  find  that  all  the 
letters  in  No.  xx  (6),  are  clearly  made  out  at  a  distance  of  20 
feet,  the  existence  of  astigmatism  in  any  abnormal  degree 
can  be  excluded. 

§  47.  If,  however,  V  does  not  reach  6/6  we  may  be  sure  of 
the  existence  of  some  error  in  refraction,  which  may  be  either 
myopia,  hypermetropia  or  astigmatism. 

In  order  to  determine  which  kind  of  ametropia  is  present, 
we  place  in  front  of  the  eye  first,  a+i  spherical  lens.  If  this 
does  not  render  the  vision  worse,  or  if  it,  on  the  contrary,  im- 
proves it,  we  are  sure  hypermetropia  exists,  and  the  strongest  -\- 

(55) 


56  DETERMINING    THE    PRESENCE    OF    ASTIGMATISM. 

lens,  through  which  No.  6  is  seen  clearly  and  distinctly,  marks 
the  degree  of  the  hypermetropia,  and,  as  V='/«i  we  may  De 
sure  that  astigmatism  does  not  exist. 

If  -}-  lenses  do  not  improve,  but,  on  the  contrary,  impair  vis- 
ion, then  we  try  spherical  concave  glasses,  and  if  we  find  one 
which  gives  V=M/M  we  may  safely  conclude  that  it  is  a  case 
of  simple  myopia,  and  the  weakest  concave  glass,  which  gives 
a  normal  acuteness  of  vision,  marks  its  degree. 

§  48.  But  if  spherical  lenses,  while  improving  V  somewhat, 
do  not  bring  the  acuteness  of  vision  up  to  the  normal  stan- 
dard of  20/»»  we  may  rightly  consider  that  astigmatism,  either 
regular  or  irregular,  is  present. 

§  49.  Persons  affected  with  regular  astigmatism  usually  give 
us  an  intimation  of  their  peculiar  refractive  error  by  the  mis- 
takes they  make  in  naming  certain  letters  of  the  test-types — 
P  and  F,  for  example,  are  very  likely  to  be  confounded ;  C  is 
often  called  G,  and  both  are  sometimes  mistaken  for  O,  while 
such  letters  as  L  and  T  are  readily  recognized. 

Dr.  W.  S.  Little  has  devised  a  "  test-card l  of  words,  made 
up  of  letters  confusing  to  the  astigmatic  eye,"  on  this  princi- 
ple, which  is  useful  for  the  purpose  of  indicating  to  us  whether 
or  not  astigmatism  exists. 

§  50.  Being  satisfied  that  astigmatism  is  present,  the  next 
step  is  to  determine  the  direction  of  the  principal  meridians. 
One  of  th*e  simplest  methods  of  ascertaining  this  is  to  turn  a 
cylindrical  glass  of  -j-  or  —  I  D  before  the  eye,  noting  the 
meridians  with  which  the  axis  of  the  cylinder  corresponds 
when  the  smallest  test  letters  of  Snellen  that  can  be  distin- 
guished are  most  and  least  distinct.  These  meridians,  which 
will  be  found  at  right  angles  to  each  other,  are  the  meridians 
of  greatest  and  least  refraction. 

§  51.  Another  plan  is  to  place  before  the  patient  a  series  of 
lines  of  equal  thickness,  radiating  from  a  common  centre,  such 
as  the  wall-known  fan  of  Snellen.  These  lines  should  be 
placed  at  such  a  distance  that  one  or  two  running  in  one  di- 
rection shall  be  seen  clearly  and  distinctly.  The  direction  of 

1  Published  by  J.  W.  Queen;&  Co./Phila. 


THE    PRINCIPAL    MERIDIANS.  57 

these  lines  will  correspond  to  one  of  the  principal  meridians, 
and  the  other  meridian  will  be  at  right  angles  to  it. 

There  are  other  methods  for  determining  the  direction  of 
the  principal  meridians,  of  which  we  shall  speak  later,  but  in 
simple,  uncomplicated  cases  these  will  suffice. 

§  52.  The  directions  of  the  principal  meridians  are  ex- 
pressed in  degrees  representing  their  inclination  to  the  hori- 
zon. Thus  :  If  we  find  that  the  line  of  Snellen's  fan  which  is 
most  distinct  is  the  vertical  or  at  90°,  the  corresponding  me- 
ridian will  be  horizontal  or  at  180°,  and  the  opposing  meridian 
vertical  or  at  90°.  If  the  axis  of  the  cylinder  which  renders 
the  test-types  clearest  is  at  45°  we  know  that  it  is  the  me- 
ridian at  135°  which  is  affected  by  its  refraction,  for  the  axis  of 
the  cylinder  is  always  at  right  angles  to  the  meridian  whose  re- 
fraction it  affects.  It  therefore  becomes  easy  to  express  ex- 
actly in  degrees  of  inclination  to  the  horizon  the  direction  of 
the  meridians  of  greatest  and  least  refraction. 

§  53.  Having  in  this  way  obtained  the  direction  of  the  prin- 
cipal meridians,  it  remains  to  determine  whether  only  one  or 
both  are  ametropic,  and  the  degree  of  the  ametropia ;  in 
other  words,  to  define  the  form  and  amount  of  astigmatism. 

This  will  be  most  easily  done  by  taking  some  cases  repre- 
senting each  of  the  three  forms  of  astigmatism. 

\  54.  CASE  I.  The  patient  has  V=--20/i  barely,  and  it  is  not  brought  up  to  20/xi  by 
any  +  or  —  glass.  By  rotating  a  -j-i  cylinder  before  the  eye,  we  find  that  when  the 
axis  is  perpendicular  or  at  90°  V=20/xxx  and  a  few  letters  of  No.  XX  are  made  out. 
When  the  axis  is  at  180°,  vision  is  very  much  worse,  so  that  he  can  scarcely  make 
out  No.  LXX.  This  shows  that  the  principal  meridians  are  vertical  and  horizontal, 
and  also  that  the  horizontal  meridian  which  corresponds  with  the  refracting  merid- 
ian of  the  correcting  cylinder  is  hypermetropic.  We  now  place  a  -(-0.507  axis  vertical 
before  the  eye,  which,  while  improving  vision  somewhat,  does  not  increase  it  as 
much  as  the  +i.  The  hypermetropia  of  the  meridian  is  therefore  greater  than  i  1). 
We  then  try  +1.5  cy,  axis  90°,  and  find  that  with  this  all  the  letters  in  No.  XX 
are  seen  distinctly,  while  with  +2  cy  axis  90°  they  are  less  distinct.  Diagnosis : 
Simple  hypermetropic  astigmatism  in  the  horizontal  meridian.  Or  we  may  express 
it  thus  :  H.  astig.  1.5  D  axis  90°;  for  it  must  always  be  borne  in  mind  that  the  axis  of 
the  cylinder  is  at  right  angles  to  the  direction  of  the  meridian  it  corrects. 

\  55.  CASE  II.  The  patient  in  looking  at  Snellen's  fan  placed  at  a  distance  of 
six  metres,  says  he  sees  only  one  or  two  black  lines  to  the  right,  all  the  others  appear- 
ing blurred.  You  find  upon  examination  that  the  line  which  is  sharpest  and  black- 


58  ILLUSTRATIVE    CASES. 

est  is  at  125°.  You  now  place  before  the  eye  a  -fi  spherical  lens  and  ask  him 
whether  this  line  still  remains  as  distinct  as  before.  If  he  answers  "No,"  then  you 
try  minus  spherical  lenses  in  the  same  way  and  if  the  line  is  not  more  distinct 
with  than  without  them,  this  meridian  (35°)  is  emmetropic.  You  then  place  plus 
glasses  before  the  eye  and  ask  their  effect  on  the  lines  to  the  left  which  are  most 
blurred,  and  if  you  find  that  they  do  not  help,  but  on  the  contrary  render  them  still 
more  indistinct,  you  try  minus  spherical  glasses  With  these  you  find  the  indistinct 
lines  to  brighten  up,  and  finally  with  —2  spherical  the  lines  at  about  35°  become 
very  clear  and  sharp,  while  those  at  125°  are  rendered  gray  and  indistinct.  This 
shows  that  the  meridian  with  its  axis  at  35°  has  a  myopia  —  2  D.  If  a  cylindrical 
lens  —  2  D  is  placed  with  its  axis  at  35°  the  fan  becomes  even,  all  the  lines  having 
the  same  clearness  and  distinctness  and  with  it  V  =  »/„.  This  is  a  case  of  simple 


DIAGRAMMATIC  REPRESENTATION  OF  THE  DIRECTION  OF  THE  Axis  OK  AN 

MATIC  MERIDIAN. 

myopic  astigmatism:  M.  astig.  =  2  D  axis  35°, "and  it  may  be  recorded  graphic- 
ally as  in  Fig.  20,  where  the  line  AB  represents  the  axis  of  the  faulty  meridian. 

{  56.  CASE  III.  Without  any  glass  V  =  '/M,  and  none  of  the  lines  in  Snellen's 
fan  are  seen  with  distinctness,  all  being  a  confused  blur.  Spherical  glasses  art-  tried 
as  in  the  other  cases,  beginning  with  the  convex,  and  it  is  found  after  a  number  of 
trials  that  with  a  — 1.5  all  the  letters  in  No.  18  are  properly  made  out,  with  the  ex- 
ception that  P  is  called  F,  and  with  this  lens  the  line  in  Snellen's  fan  at  60°  is  quite 
sharply  defined.  Those  near  the  bottom  to  the  right,  however,  are  very  indistinct. 
If  this  is  the  weakest  concave  glass  through  which  the  line  at  60°  is  sharply  defined, 
then  the  meridian  with  its  axis  at  60°  is  myopic  to  the  extent  of  1.5  dioptrics. 

It  is  found  on  further  trial  that  the  line  at  150°  is  brought  out  clearly  by  — 3.  all 
the  others  appearing  less  distinct.  This  shows  that  the  meridian  whose  axis  lies  at 
150°  is  also  myopic.  Both  meridians  are  therefore  myopic,  but  one  in  a  higher  de- 
gree than  the  other.  The  difference  in  the  degrees  (3  —  1.5  =  1.5)  of  myopia  in 
the  two  meridians  constitutes  the  astigmatism  of  the  eye.  Because  there  is  a  spher- 
ical ametropia  associated  with  the  astigmatism,  this  form  is  called  compound  myopic 
astigmatism,  and  we  record  it  thus:  M.  1.5  D  with  M.  astig.  1.5  axis  150°.  Writh 
this  combination  of  minus  glasses  the  fan  appears  uniform  and  vision  =  6/s. 


ILLUSTRATIVE    CASES, 


59 


\  57.  CASE  IV.  We  find  that  the  patient,  who  is  a  boy  of  15,  sees  the  line  of  the 
fan  at  170°  more  clearly  than  any  of  the  others.  He  can  also  see  it  clearly  with  a 
— Vie  or  a  +Vis  spherical.  This  shows  that  there  is  hypermetropia  in  the  corre- 
sponding meridian,  and  thai  he  overcomes  the  —  glass  by  means  of  his  accommoda- 
tion, which  is  very  strong  at  that  age.  A  +  Vie  or  +  Vis  blurs  this  line,  therefore 
meridian  with  its  axis  at  170°  has  H  =  Vis-  With  this  glass  the  indistinct  lines  on 
the  left  near  the  centre  also  appear  brighter  and  with  a  +Vio  they  are  perfectly 
clear,  the  blackest  one  being  at  80°  ;  that  at  170°  is  very  much  blurred.  We  have, 
therefore,  a  H.  in  the  meridian  80°  which  is  greater  than  that  in  the  meridian  at  right 
angles  to  it.  There  being  hypermetropia  in  both  meridians  but  more  in  one  than  in 
the  other,  this  is  compound  hypermctropic  astigmatism,  and  as  both  have  H.  =  Vis 


METHOD  OF  RECORDING  A  CASE  OF  COMPOUND  ASTIGMATISM. 


in  common,  we  write  H.— Vis  with  H.  astig.=Vio-*-Vi8=18/i80 — w/iati=^/iti<f=-1/n,  axis 
80°,  or  represent  it  graphically  as  in  Fig.  21.  This  example  shows  the  great  disad- 
vantage of  the  old  inch  system  in  making  subtraction  and  addition  of  lenses,  which 
we  have  so  frequently  to  do  in  determining  astigmatism. 

With  this  combination  of  lenses  V  —  20/2o  and  all  the  lines  in  Snellen's  fan  are 
distinct. 

\  58.  CASE  V.  The  patient  has  very  bad  vision,  not  being  able  to  make  out  No. 
60  at  6  metres.  Some  — glasses,  Vs»  Ve  or  VT>  increase  it  slightly  and  +  glasses  up 
to  V»2  do  not  make  vision  worse.  On  asking  him  to  look  at  the  fan  we  find  that  all 
is  indistinct,  but  he  thinks  he  sees  a  vertical  line,  though  it  is  much  blurred.  We 
place  spherical  glasses  in  succession  before  the  eye  as  usual,  and  after  many  trials 
find  that  the  line  at  90°  comes  out  sharply  with  +J/22,  while  those  at  the  bottom  are 
so  confused  that  they  cannot  be  recognized  as  lines  at  all.  We  are  now  assured  that 
90°  is  the  axis  of  the  hypermetropic  meridian.  The  meridian  whose  axis  is  at  180° 
we  know  is  not  hypermetropic,  because  the  horizontal  lines  are  more  blurred  through 
the  convex  lenses.  We  therefore  try  minus  glasses  for  this  meridian,  and  after  a 


6O  ILLUSTRATIVE    CASES. 

number  oi  trials  find  that  the  line  at  180°  is  sharp  and  black  with  — '/«,  the  other 
lines  appearing  as  a  grey  blur.  There  is  therefore  a  M.  of  '/«  'n  this  meridian. 
There  being  H.  in  the  horizontal  meridian  and  M.  in  the  vertical  meridian  we  have 
to  deal  here  with  a  case  of  mixed  astigmatism  and  we  write  II.  =  '/w  9°°  with  M. 
=  '/•  1 80°.  The  Mai  astigmatism  is  therefore  equal  to  the  sum  of  these,  that  is 
VM  +  '/•  =  '/is*  +  */i»  =  "/i«  =  '/4-75.  With  this  combination  of  lenses  (+  '/n 
90°  O  — '/•  180°)  V  =  '/•  and  all  the  lines  in  the  fan  become  of  uniform  clearness. 

§  59.  In  simple,  uncomplicated  cases  the  methods  employed  in 
the  foregoing  examples  are  sufficient,  if  carefully  followed  out,to 
establish  the  diagnosis  and  the  character  of  astigmatism,  and, 
under  all  circumstances,  by  whatever  method  the  diagnosis  of 
the  astigmatism  may  have  been  determined,  it  must  be  veri- 
fied by  means  of  cylindrical  lenses  and  the  test-types.  The 
best  vision  is  what  we  aim  at,  and  no  method  has  yet  been 
found  which  can  dispense  with  this  as  the  final  arbitrament. 

§  60.  But,  unfortunately,  all  cases  of  astigmatism  are  not 
uncomplicated,  and  there  are  many  ways  in  which  error,  both 
on  the  part  of  the  patient  and  surgeon,  may  creep  in. 

The  sources  of  these  errors  will  be  considered  in  the  next 
following  chapter. 

BIBLIOGRAPHY. 


Raudon — Note  sur  un  moyen  prat,  de  reconnaitre.  i.  L'astig  reg.  2.  La  nature  de 
1'astig  h.  ou  m.  3.  Le  meridian  astigmate.  4.  Le  degre  de  1'astig.  sans  les  verres 
cylind.  par  1'emploi  exclusif  des  verres  spheriques.  Rec.  d'Ophth.  P.  8l.  1878. 

Buckner,  J.  H. — Astig.,  illust.  cases  from  clinic,  mem.  Cincin.  Lancet  and  Obs. 
Aug.  P.  466.  1875. 

Carreras— Del  Astig.  Compilador  Med.  Barcelona.  IV.  Pp.  283,  301,  389. 
1868.  V.  Pp.  89, 91.  1869. 

Culbertson,  H. — Refract,  of  the  eye  as  distinguished  from  accommodat.  and  esti- 
mated as  an  equivalent  from  the  index  of  refract.  Cincin.  Lancet  and  Clinic.  VIII. 
P.  451.  1882. 

Daumas,  L.  C.— De  1'astig.    4°.     Paris.     1874. 

Derby,  H.— Four  cases  of  astig.  Am.  M.  Times.  New  York.  VII.  Pp.  277-78. 
1863. 

Donders,  F.  C.— L'astig.    Arch.  gen.  de  Med,     I.     Pp.  200-9.     Paris.     1863. 

Fenner,  C.  J.— A  treatise  on  refract,  and  accommodat.  Richd.  and  Louisville 
Med.  Jr.  P.  481.  1873. 

Ferguson,  R.  M. — On  a  remark,  case  of  astig.  Louisvl.  Med.  Times.  Dec.  1 5. 
1883. 


BIBLIOGRAPHY.  6l 

Fravel,  E.  H.— Anom.  of  Refract.  Gaillard's  M.  Jr.  New  York.  XXXII.  P.  442. 
1882. 

Frothingham,  G.  E. — A  case  of  mixed  astig.  with  predom.  myopia,  diagnosed  by 
its  very  peculiar  ophth.  appearance.  Phys.  and  Surg.  Ann  Arbor,  Mich.  II.  Pp. 
14-16.  1880. 

Fulton,  J.  F. — Astig.:  a  rept.  of  cases.  N.  W.  Lancet.  St.  Paul,  Minn.  II.  Pp. 
3-6.  1882. 

Galezowski — De  quelques  varietes  d'astig.  Rec.  d'Ophth.  Paris.  II.  Pp.  464- 
1874. 

Grossmann,  L. — Die  Accommodat.  u.  Refract-lehre.  Med.  Chir.  Presse.  Pest. 
Nos.  10,  11,  12,  14.  1873. 

Hafften,  van,  Wm. — Die  Bestimmg.  des  Astig.     Utrecht.     1879. 

Harlan,  G.  C. — Co.  myop.  astig.     Phila.  M.  Times.     II.     P.  70.     1871. 

Hays,  Isaac— Astig.     Tr.  Coll.  Phys.     Phila.     N.  S.     I.     P.  418.     1850. 

Higgins,  C. — Astig.     Med.  Times  and  Gaz.     II.     Pp.  669-71.     London.     1876. 

Hirschberg,  J. — Refraktion.  Eulenberg's  real  Encyp.  d.  ges.  Heilkd.  XI.  P. 
379-  1882. 

Hough,  J.  B. — On  the  detect,  and  estim.  of  astig.  Cincin.  Lancet  and  Obs.  XVII. 
Pp.  262-4.  1874. 

Hulke,  J.  W. — Summary  of  192  cases  of  astig.  Ophth.  Hosp.  Rep.  VIII.  Pp. 
141-77.  London.  1875. 

Imbert — De  1'astig.     Paris.     1883. 

Javal,  E.— De  1'astig.  (Rap.  de  M.  Gavarret).  Bull.  Acad.  de  Med.  XXXII.  Pp. 
872-82.  Paris.  1866-7. 

Javal,  E. — Nouvelle  install,  pour  la  determinat.  de  1'astig.  Ann.  d'Oculist.  T. 
LVII.  P.  37.  1867. 

Javal,  E.— De  ia  lentille  de  Stokes.     Ann.  d.  Oculist.     T.  LXI.     P.  73.     iF6g. 

Javal,  E. — Divers  appareils  pour  la  measure  de  1'astig.  Compt.  rend,  de  la  Soc. 
de  Biolog.  P.  302.  1873. 

Javal,  E. — Des  variations  de  1'astig.  Compt.  rend,  de  la  Soc.  de  Biolog.  55.  V. 
P.  270.  1874. 

Javal,  E.— Lentille  de  Stokes  modifiee,     Ann.  d'Oculist.  T.  LXXX.  P.  201.  1878. 

Kaiser,  H. — Die  Theorie  des  Astig.  Graeles  Arch.  XI.  Hft.  3.  Pp,  186-229. 
1865. 

Knapp,  H. — Demonstrat.  of  the  refract,  of  light  by  asymet.  surfaces  and  the  deter- 
minat. of  astig.  with  glasses  and  the  ophthalms.  Trans.  Am.  Med.  Ass.  1880. 

Knauthe,  T.  H.— Ueber  Astig.     8°.     Leipzig.     1863. 

Landesberg,  M.— Regl.  Astig.     Med.  Bull.     Phila.     III.     Pp.  256-8.     1881. 

Little,  W,  S. — A  tabl.  rept.  exhibit,  the  position  of  the  axis  of  the  cylind.  in  simpl. 
co.  and  mxd.  astig.,  the  m.  and  h.  forms  compared,  with  rmks.     Trans.  Amer.  Oph.  • 
Soc.     1880. 

Magin — Dell  'ipermetrop.  e  dell'astig.     Riv.  Clin.  di  Bologna.    V.  Pp.  85-9.  1866. 

Mauthner,  L. — Vorlesungen  ii.  d.  optisch.  Fehler  d.  Auges.  Wien.  W.  Braumuller. 
1876. 

Mengin — Astig.  mixte  a  droite  ;  hypermetrop.  simple  a  gauche,  Rec.  d'Ophth. 
3.  S.  II.  Pp.  1 7-20.  Paris.  1880. 

Meyer,  E.— De  1'astig.     Gaz.  des  Hop.     XXXIX.     P.  342.     Paris,  1866. 

Middleburg,  H.  A. — De  Zitplaats  van  het  Astig.  versl.  Nederl.  Gasth.  v.     Ooglig- 


62  BIBLIOGRAPHY. 

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P.  83. 

Nagel— Die  Anomal.  der  Refract  u.  Accommodat.  des  Auges.  Graefe  u.  Sae- 
mish.  Hdb.  d.  gesmt  Aughlk.  B.  VI.  Cap.  X. 

Nicalaysen,  J.— Om.  Astig.  Norsk,  mag.  f.  Laegevidensk.  XX.  Pp.  721-41. 
Christian  ia.  1 866. 

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Noyes,  H.  D. — A  scheme  to  aid  in  recording  and  examining  cases  of  asthenop. 
Trans.  Amer.  Ophth.  Soc.  Pp,  81-7.  1871. 

Perrin,  M.— Astig.    J.  d'Ophth.     I.     Pp.  54,  112,  148.     Paris.     1872. 

Reeve— On  optic,  defects.    Trs.  Canad.  Med.  Assoc.     I.     P.  192.     1877. 

Risley — A  case  of  hypermetrop.  astig.     N.  Y.  Med.  Jr.  V.  XL.  No.  5. 

Salen,  E.— Om  Astig.     Upsala  Lakaref.     Forh.     III.     Pp.  457-8'-     1867-8. 

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Snellen,  H. — De  Richtung  der  Hauptmerid.  des  astig.  Auges  Graefe's  Arch.  XV. 
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Wien.  1866. 

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Ztschr.  f.  vergleich.  Augenhlk.  1882. 


CHAPTER   V. 


DIFFICULTIES  AND  OBSTACLES  IN  THE  WAY  OF  AN  ACCURATE 
DIAGNOSIS  OF  ASTIGMATISM — INFLUENCE  OF  ACCOM- 
MODATION— THE  USE  OF  MYDRIATICS. 

§  61.  As  stated  in  the  concluding  paragraph  of  the  last 
chapter,  all  cases  of  astigmatism  are  not  so  readily  determined 
as  might  appear  from  the  examples  given.  The  inexperienced 
beginner  will  meet  with  many  perplexities,  and  there  are  cases 
which  test  the  skill  even  of  the  most  expert. 

We  shall  endeavor  in  this  chapter  to  point  out  the  principal 
obstacles  that  lie  in  the  way  of  a  correct  and  speedy  diagnosis 
and  the  best  methods  for  overcoming  them. 

§  62.  Most  of  the  difficulties  arise  from  the  fact  that  we  are 
not  dealing  with  an  optical  instrument  alone,  but  also  with  an 
anatomical  organ  having  a  physiological  function.  It  is  the 
office  of  the  eye,  as  an  organ  of  sense,  to  interpret  impressions 
made  on  the  retina,  and  the  judgments  formed  from  these  im- 
pressions are  not  always  correct.  It  is  astonishing  how  often 
otherwise  intelligent  persons  will  make  statements  as  to  what 
they  see,  which  we  know  are  not  true,  and  which,  upon  further 
questioning  and  coaching,  they  reverse.  As  a  matter  of  ex- 
perience, we  find  that  most  astigmatic  patients  have  to  be,  to  a 
greater  or  less  extent,  educated  in  the  right  method  of  observ- 
ing and  of  correctly  reporting  what  they  see,  and  it  often  re- 
quires the  exercise  of  much  patience  on  the  part  of  both  ex- 
aminer and  patient  to  arrive  at  the  exact  truth.  The  answers 
to  questions  are  frequently  misleading,  and  much  tact  is  fre- 
quently necessary  to  extract  the  true  meaning  from  statements 
which,  though  honestly  given,  are  incorrect.  And  besides,  the 
answers  are  often  of  such  a  vague  and  general  character  that 

(63) 


64  SOURCES   OF    ERROR    IN    DIAGNOSIS. 

opposite  interpretations  might  be  given  to  them,  and  it  is 
never  safe  to  trust  to  the  results  of  a  first  examination.  Sev- 
eral trials  should  be  made  with  different  lenses  with  their  axis 
at  various  degrees  until  there  is  found  one  which,  when  placed 
at  the  same  angle,  always  gives  the  same  and  the  best  result. 

When,  in  a  compound  myopic  astig.,  the  common  M.  being 
3D,  a  minus  spherical  lens  of  that  strength  is  held  before  the  eye 
and  the  patient  is  told  to  look  at  the  fan  he  will  most  likely 
say  that  he  sees  nothing.  Upon  close  questioning,  however, 
we  find  that  he  does  see  a  single  line,  and  this  single  line  is 
perhaps  the  key  to  the  situation.  And  when,  on  the  other 
hand,  in  simple  astigmatism  of  either  form,  a  cylindrical  lens  of 
the  proper  kind,  but  under  or  over-correcting,  is  so  placed  before 
the  eye  that  its  axis  shall  correspond  with  that  of  the  faulty 
meridian,  the  patient  may  exclaim,  "Now  I  see  all  the  lines." 
That  may  be  true,  but  it  may  not  be  all  we  want.  It  is  neces- 
sary not  only  that  he  see  them  all,  but  that  he  see  them  all 
with  equal  clearness  and  distinctness.  Other  cylindrical 
lenses  of  the  same  character  must  be  tried  until  one  is  found 
with  which  the  fan  is  said  to  appear  uniform.  But  even  this 
should  not  be  entirely  trusted.  The  test-letters  must  be 
the  final  resort,  and  glasses  weaker  and  stronger  than  the  one 
selected  must  be  tried  to  see  whether  vision  is  made  better  or 
worse  by  them. 

§  63.  We  find,  under  certain  circumstances,  an  improvement 
with  cylindrical  glasses  when  there  is  no  astigmatism  present. 
A  person  having  M  =  !/i§  with  V  =  *%,  will  find  vision  so 
much  improved  by  a  —'/is  cy.  that  some  letters  in  No.  L  can  be 
made  out.  This  improvement  does  not  come  from  the  cor- 
rection of  an  astigmatism,  but  is  due  to  a  correction  of  the 
myopia  in  one  meridian,  thus  transforming  a  M.  of  Vis  mto  a 
M.  astg.  of/is,  in  which  one  meridian  is  emmetropic;  and  an 
ametropia  in  a  single  meridian  is  much  better  for  vision  than 
an  ametropia  in  both.  Under  these  circumstances,  too,  vision 
remains  the  same  when  the  lens  is  rotated  with  its  axis  in  va- 
rious meridians,  which  is  not  the  case  in  astigmatism. 

In  making  examinations  by  these  methods,  therefore,  trials 


INFLUENCE    OF    THE    ACCOMMODATION.  6$ 

with  spherical  glasses  should  always  be  made  first,  and  if  they 
do  not  bring  vision  up  to  the  normal  standard  then  search 
should  be  made  for  astigmatism. 

§  64.  It  is  believed  by  some  that  astigmatics  used  by  pref- 
erence the  centre  of  their  focal  interval,  or  rather  that  portion 
whose  section  is  a  circle,  as  shown  in  E,  Fig.  12.  This  can 
hardly  be,  for  the  eye  instinctively  seeks  to  have  a  distinct 
image,  if  it  is  possible,  of  some  part  of  an  object,  rather  than 
a  confused  image  of  the  whole.  It  is  natural,  therefore,  that 
they  should  use  one  or  the  other  focal  line  when  it  is  possible 
for  them  to  do  so.  Which  focal  line  they  prefer  when  they 
have  both  at  command  has  not  been  determined  definitely, 
but  it  would  seem  that  theoretically  they  would  select  the 
anterior  focal  line,  because  here  the  circles  of  diffusion  are 
smaller  than  at  the  posterior  focal  line  (§  19).  Certain  ob- 
served cases  appear  to  corroborate  this  view.  I  have  seen 
several  cases  of  simple  hypermetropic  astigmatism  with  the 
axis  at  90°  which  had  been  converted  by  a  tonicity  of  the 
ciliary  muscles  into  a  simple  myopic  astigmatism  axis  180°, 
thus  rendering  90°  emmetropic.  I  accounted  for  it  by  sup- 
posing that  they  preferred  to  always  have  vertical  lines  dis- 
tinct. It  may  be  stated,  in  this  connection,  that  the  small  de- 
gree'of  accommodation  possessed  by  some  aphakial  eyes  which 
enables  them  to  have  an  amount  of  distinct  vision  with  the 
same  glasses  at  different  distances,  has  been  explained  by  an 
astigmatism  which  enables  them  to  see  one  part  of  an  object 
more  clearly  at  one  distance  and  another  part  at  another. 
Their  range  of  A  would  be  expressed  by  their  degree  of  astig- 
matism. 

§  65.  But  aside  from  these  sources  of  error  there  is  another 
still  more  important,  which  arises  from  the  power  possessed 
by  the  eye  of  changing  its  refractive  condition  at  will.  This 
faculty  of  "accommodation"  (A)  resides  in  the  ciliary  mus- 
cle, and  the  change  is  brought  about  by  its  action  on  the  crys- 
talline lens,  causing  it  to  become  more  convex,  thus  increas- 
ing its  refracting  power.  It  will  be  seen,  on  a  moment's  con- 
sideration, that  the  accommodation  becomes  an  important 


66  INFLUENCE    OF   THE    ACCOMMODATION. 

factor  in  determining  the  static  refraction  of  the  eye — that  is 
the  refractive  condition  when  in  a  state  of  absolute  repose.  In 
examinations  of  the  eye  as  regards  its  optical  properties  its 
dynamic  refraction  must  always  be  held  in  mind  as  a  possible 
element,  and  its  influence  allowed  for.  This  is  not  the  proper 
place  to  consider  the  influence  of  the  accommodation  on  all 
the  forms  of  ametropia,  so  we  shall  limit  ourselves  to  the  ef- 
fects as  we  find  them  in  astigmatism. 

§  66.  Since  the  effect  of  the  accommodation  is  to  increase 
the  refraction  of  the  eye,  we  know  in  what  direction  to  look  for 
its  influence.  Such  an  increase  of  refracting  power  would  di- 
minish the  degree  of  a  hypermetropia,  convert  it  into  an  em- 
metropia,"or  even  into  a  myopia.  It  would  change  an  emme- 
tropia  into  a  myopia,  and  where  myopia  existed  increase  its 
degree.  It  would  in  the  same  manner  change  not  only  the  de- 
gree, but  also  the  form  of  an  astigmatism.  A  compound  hy- 
permetropic  astigmatism  can  be  changed  by  the  act  of  accom- 
modation into  the  simple  hypermetropic  form,  into  the  simple 
form,  or,  it  may  be,  into  the  compound  myopic  form.  Mixed 
astigmatism  may  be  masked  by  the  accommodation,  being 
converted  into  the  simple  or  the  compound  myopic  form. 

Take  for  example,  H  =  3  ^  H.  astig.  =  2  axis  90°.  An 
amount  of  A  equal  to  3  D  would  convert  this  into  a  H.  astig. 
=  2  D ;  that  is  to  say,  an  increase  of  refraction  of  3  D  would 
render  the  meridian  with  its  axis  at  1 80°  emmetropic  and 
leave  a  H  =  2  D  at  90°.  If  A  =  5  D,  then  the  meridian  with 
its  axis  at  90°  would  be  rendered  emmetropic  while  that  at 
1 80°  would  be  myopic  by  5  —  3  =  20,  converting  it  into  a 
case  of  simple  M.  astig.  Should  A  =  6  D  it  would  be  a  com- 
pound myopic  astig.:  M  =  i  ^  M.  astig  =  3  axis  180°. 

In  testing  for  astigmatism,  therefore,  due  care  must  be  ex- 
ercised in  eliminating  any  complications  on  the  part  of  the 
accommodation.  It  is  for  this  reason  that  we  use,  by  prefer- 
ence, those  methods  of  examination  in  which  the  patient  is  re- 
moved to  5  or  6  metres  from  the  test  objects.  Under  these 
circumstances  the  emmetropic  eye  is  in  a  state  of  repose  and 
adapted  to  the  parallel  rays  which  come  from  objects  at  that 


USE    OF    ATROPINE.  6/ 

.<••  r  distance,  and  there  is  no  incentive  for  the  exercsie  of  the  accom- 
modative power ;  while  in  the  case  of  myopia  the  accommoda- 
tion would  be  of  no  avail,  since  the  myopic  eye  has  al- 
ready an  excess  of  refraction,  and  its  far  point  is  nearer  than 
20  feet.  So  we  have,  in  this  method,  to  take  only  a  possible 
hypermetropia  into  consideration.  Under  ordinary  circum- 
stances, and  where  there  is  no  actual  spasm  or  undue  to- 
nicity  of  the  ciliary  muscle,  there  need  be  no  important  error 
from  this  source,  if  proper  care  is  exercised  and  sufficient  time 
is  given  to  the  investigation. 

§  67.  Examinations  should  always  begin  with  convex .  lenses  ; 
and  myopic  conditions  should  never  be  accepted  unless  there 
is  an  improvement  with  concave  glasses,  which  no  other  glasses 
give.  When,  for  example,  we  find  that  —  I  cy.  with  the  axis 
at  1 80°  brings  vision  from  20/50  to  20/20,  we  must  not  conclude 
that  we  have  to  do  with  a  case  of  simple  myopic  astigmatism, 
particularly  if  the  patient  be  a  young  person  with  an  active  ac- 
commodation. It  might  be  that  the  —  I  cy.  180°  had  con- 
verted a  simple  H.  astig.  of  I  D  90°  into  a  simple  hypermetro- 
pia ot  i  D,  which  the  accommodation  could  readily  overcome. 
In  this  instance  it  is  true  the  astigmatism  would  have  been  cor- 
rected, but  at  the  expense  of  the  accommodation  power.  So 
before  concluding  a  diagnosis  of  M.  astig.  we  should  try  the 
effect  of  a  +  i  cy.  90°,  and  if  with  this  V  =  20/20  we  know 
positively  that  it  is  H.  astig.  of  I  D  axis  90°. 

§  68.  There  is  a  way  by  which  we  can  with  certainty  get 
rid  of  the  errors  that  arise  from  the  accommodotion.  By  par- 
alyzing the  ciliary  muscle  by  some  of  the  mydriatics  such  as 
atropine,  duboisine,  homatropine,  etc.,  we  eliminate  its  active 
or  dynamic  refraction,  and  place  the  eye  in  a  condition  of 
static  refraction,  though,  as  we  shall  see  later,  this  is  not  al- 
ways its  normal  optical  state  of  repose.  When  a  drop  of  a  2 
or  4%  solution  of  atropine  is  put  in  the  eye,  in  from  twenty 
minutes  to  half  an  hour  there  is  great  dilatation  of  the  pupil, 
followed  some  minutes  later  by  a  loss  of  the  whole  or  a  greater 
part  of  the  power  of  accommodation.  When  there  is  spasm 
or  undue  tonicity  of  the  ciliary  muscle  it  frequently  requires 


NORMAL    OPTICAL    STATE    OF    REPOSE. 

several  instillations  practiced  at  intervals  of  an  hour  or  so  to 
produce  a  complete  relaxation  of  the  muscle,  and  some- 
times it  takes  several  days,  with  from  four  to  six  instillations 
each  day,  to  obtain  the  full  effect  of  the  drug. 

§  69.  But  while  this  paralysis  of  the  ciliary  muscle  gives  us 
a  relief  from  disturbances  on  the  part  of  the  accommodation, 
it  is  in  itself  not  entirely  free  from  disadvantages,  inconveni- 
ences, and  even  errors. 

One  of  the  chief  inconveniences  attendant  upon  paralysis  of 
A  is  that  the  effect  of  the  mydriatic  does  not  pass  off  fully 
within  a  week,  and  often  ten  or  twelve  days  elapse  before  the 
ciliary  muscle  regains  its  normal  tone.  During  this  time  the 
patient,  unless  highly  myopic,  is  deprived  of  the  use  of  the 
eyes  for  all  close  work,  such  as  reading,  writing,  etc.,  and  this, 
to  the  large  majority  of  our  patients,  is  a  matter  of  great  mo- 
ment. We  have  no  right  to  deprive  a  patient  of  all  use  of  the 
eyes  for  a  week  if  it  can  be  avoided. 

Besides,  the  result  obtained  by  an  examination  under  this 
condition  does  not  represent  always  the  actual  and  normal 
static  refraction  of  the  eye.  A  paralyzed  state  of  a  muscle  is 
not  its  normal  condition.  There  is  a  certain  amount  of  to- 
nicity  inherent  in  every  muscle  which  disappears  when  it  is 
paralyzed,  and  it  is  unquestionably  a  varying  quantity  in  differ- 
ent individuals.  As  a  result  of  this,  we  find  that  when  the  A 
of  young  people  is  paralyzed  there  is  a  diminution  of  static 
refraction  varying  from  0.5  D  to  2  D.  It  is  the  custom  to  re- 
fer to  this  as  the  latent  hypermetropia,  and  so,  in  a  certain 
sense,  it  is,  but  it  is  doubtful  whether  we  should  under  ordi- 
nary circumstances,  and  when  it  is  low  in  degree  look  upon  it 
as  pathological  or  abnormal.  The  result  of  an  examination  of 
the  refraction  of  a  large  number  of  children,  ranging  in  age 
from  a  few  hours  to  10  and  12  years,  seems  to  point  to  the 
fact  that  in  the  human  eye  we  have  from  infancy  to  adult  life 
a  gradual  evolution  from  the  hypermetropic  to  the  emmetropic 
and  myopic  condition.1  Dantel,  from  the  results  of  an  exam- 

1  It  is  a  significant  lact  in  this  direction  that  the  eyes  of  most  lower  animals  are 
hypermclropic — some  of  them  very  highly  so. 


LATENT    HYPERMETROPIA.  69 

ination  of  a  large  number  of  persons  of  all  ages  as  to  their 
manifest  and  total  hypermetropia,  finds  that  only  l/3  of  the  to- 
tal H  is  manifest  from  6  to  15  years;  l/2  from  16  to  25  ;  2/3~V* 
from  26  to  35,  and  the  two  are  equal  only  after  the  36th  year. 
He  finds  also,  as  a  matter  of  experience,  that  in  eyes  other- 
wise sound  a  correction  of  manifest  H  is  quite  sufficient. 
With  the  rarest  exceptions,  all  infants  are  hypermetropic,  and 
few  children  of  even  10  years,  but  show  much  decrease  of 
their  refraction  on  paralysis  of  the  accommodation.  This  hy- 
permetropia is  overcome,  as  a  rule,  by  the  normal  tonicity  of 
the  ciliary  muscle,  which  I  do  not  think  we  have  a  right  to 
regard  in  the  light  o(  a  pathological  muscular  spasm. 
When  the  ciliary  muscle  is  paralyzed  by  a  drug  its  natural 
tonicity  is  of  course  lost,  and  we  have  a  correspondingly  di- 
minished refraction,  but  when  the  effect  passes  off,  the  tonicity 
returns  and  with  it  increased  refraction,  and  the  eye  resumes 
its  previous  optical  state. 

That  there  is  such  a  tonicity  in  the  external  muscles  of  the 
eye  which  is  lost  in  paralysis,  is  clearly  demonstrated  by  the  ex- 
ophthalmus,  often  very  marked,  which  accompanies  a  paraly- 
sis of  all  the  external  muscles  of  the  eye. 

We  have  no  means  of  measuring  the  amount  of  muscular 
tonicity,  normal  to  the  eye  in  any  given  case,  for  it  is  a  ques- 
tion of  physiological  dynamics  and  we  aje  not  dealing  with  a 
constant  quantity.  The  actual  power  resident  in  the  ciliary 
muscle  does  not  seem,  in  some  cases,  to^bear  any  definite  rela- 
tion to  the  muscular  power  of  the  other  parts  of  the  body. 
We  sometimes  find  it  weak  in  strong  persons,  and  occasionally 
disproportionately  strong  in  weak  persons,  though,  as  a  gen- 
eral rule,  it  participates  in  a  general  muscular  debility. 

It  is  apparent  from  this  that,  in  young  people  particularly, 
we  should  not,  as  a  rule,  accept  the  refraction  found  under  the 
full  effect  of  a  mydriatic  as  the  normal  optical  state  of  the 
eye.  When,  therefore,  there  is  ametropia  present  with  the 
astigmatism  which  requires  correction,  the  final  glasses  should 
not  be  ordered  until  a  careful  examination  is  made  after  the 
effect  of  the  drug  has  passed  away,  for  in  the  majority  of  cases 


JO  SPASM    OF    THE    CILIARY    MUSCLE. 

in  young  persons,  the  glasses  which  correct  while  under  the 
mydriatic,  over  correct  when  the  eye  returns  to  its  natural 
state,  and  at  the  beginning,  almost  without  exception,  the 
glasses  giving  full  correction  prove  unsatisfactory,  for  one  rea- 
son, among  others,  that  the  equilibrum  between  the  external 
and  internal  muscles  to  which  the  eyes  have  accustomed  them- 
selves is  destroyed,  and  it  requires  often  a  considerable  time 
for  them  to  become  adjusted  to  the  new  order  of  things. 

§70  As  to  the  frequency  of  true  spasm  of  the  ciliary  muscle, 
the  opinions  of  clinicians  are  somewhat  divided.  Most  of  the 
continental  authorities  do  not  consider  it  at  all  common,  and, 
therefore,  except  on  rare  occasions,  do  not  follow  the  practice 
of  atropinization  before  taking  the  refraction.  Mauthner  (opt. 
Frh.  d.  Aug.,  p.  736),  contends  that  the  eye  invariably  shows 
its  true  static  refraction  under  the  ophthalmoscope.  Hirsch- 
berg  says  ( CentralbL  f.  prak.  Augenheilk.  June,  1884,  p.  169) 
that  in  the  many  thousands  of  cases  that  he  has  examined  by 
the  direct  ophthalmoscopic  method  and  with  glasses,  he  has 
never  met  with  a  case  of  spasm.  Furthermore,  he  says  that 
he  has  never  found  the  objective  refraction  different  before  and 
after  atropinization,  either  in  hypermetropia  or  in  myopia. 
Landolt  (Traite  d*  ophthalmol.  par  Wecker  et  Landolt  Tome  3) 
says  he  rarely  has  recourse  to  atropine  for  the  determination 
of  astigmatism. 

In  America,  however,  it  has  become  a  custom  with  quite  a 
number  to  resort  to  atropinization  as  a  routine  practice  in  all 
cases. 

It  should  be  the  aim  of  the  ophthalmic  practitioner  to  at- 
tain such  skill  in  the  determination  of  refraction  that  he  shall 
have  accuracy  in  his  results  at  a  minimum  of  inconvenience  to 
his  patients.  The  best  method,  it  seems  to  me,  is  to  obtain 
the  best  results  possible  by  the  methods  already  described,  or 
such  a  combination  of  those  that  will  be  described  later  as 
may  be  deemed  necessary,  and  give  the  glasses  thus  indicated 
for  trial.  If  these  should  not  prove  satisfactory,  we  have  still 
atropinization  left.  And  as  we  study  our  different  methods 
more  closely  and  acquire  by  experience  a  greater  skill  in  their 
use,  we  will  find  less  and  less  need  for  the  mydriat/c. 


PARTIAL    SPASM    OF    A.  71 

§71.  My  own  guide  to  the  use  of  atropine,!  find  in  the  di- 
rect method  of  examination  by  the  ophthalmoscope.  (See 
Chap.  VII.)  If  I  find  the  patient  to  persistently  refuse  + 
glasses,  and  yet  there  is  a  hypermetropia  manifest  under  the 
ophthalmoscope,  or  if,  while  looking  at  the  fundus  through  -f- 
glasses,  I  see  the  vessels  becoming  alternately  clear  and  indis- 
tinct, indicating  an  alternate  relaxation  and  contraction  of  the 
ciliary  muscle,  I  know  that  there  is  an  excessive  tonicity  of 
the  ciliary  muscles  which  masks  a  hypermetropia,  and  then  I 
usually  use  atropine  in  order  to  discover  to  what  extent  the 
tonicity  reaches;,  not  necessarily  for  its  full  neutralization,  but 
as  a  guide  in  the  selection  of  glasses  that  can  probably  be 
worn  with  comfort  and  advantage. 

For  the  beginner,  however,  particularly  when  the  case  is 
complicated  and  the  answers  given  by  the  patient  are  confus- 
ing and  unreliable,  and  where  the  results  by  one  method  of  ex- 
amination do  not  correspond  with  those  by  another,  an  imme- 
diate paralysis  of  A  may  be  the  shortest  way  to  a  solution  of 
the  difficulty. 

§  72.  What  has  been  said  in  the  foregoing  paragraphs  in  re- 
gard to  the  accommodation,  has  reference  to  the  contraction  of 
the  ciliary  muscle  as  a  ivhole,  and  to  its  influence  on  the  ame- 
tropia  which  may  accompany  astigmatism.  The  accommoda- 
tion in  its  entirety  cannot  affect  the  amount  of  astigmatism, 
though  it  greatly  modifies  its  general  character.  It  would  seem 
however,  from  the  reports  of  Drobowolski,  Javal  and  others, 
that  there  can  be  a  partial  contraction  of  the  muscle  of  accom- 
modation producing  a  lenticnlar  astigmatism,  the  effect  of 
which  would  be  either  to  create  a  new  or  increase  an  existing 
astigmatism,  or  to  a  greater  or  less  extent  to  neutralize  that  of 
the  cornea.  According  to  Javal  the  latter  would  appear  to  be 
the  most  common  effect,  for  he  has  found  corneal  astigmatism 
as  discovered  by  means  of  the  ophthalmometer,  overcome  by 
an  unequal  accommodation,  and  made  manifest  only  on  com- 
plete paralysis  of  the  ciliary  muscle.  To  this  unequal  contrac- 
tion of  the  ciliary  muscle  he  refers  those  cases  of  astigmatism 
which  make  their  appearance  in  adult  life  and  which  give  no 


72  DISADVANTAGES    OF    A    WIDE    PUPIL. 

evidence  of  their  existence  in  childhood.  The  unequal  A  seems 
to  pass  away  with  the  increasing  stiffness  of  the  muscle  and  the 
hardening  of  the  lens  which  are  the  accompaniments  of  advanc- 
ing years. 

§73.  In  treating  of  refraction  by  triaxial  ellipsoids  in  Chap. 
II.  it  was  shown  in  Figs.  7  and  8  that  the  monochromatic  abe- 
rration of  the  cornea  increased  from  the  apex  towards  the 
periphery,  and  from  this  arises  another  disadvantage  attendant 
on  the  use  of  a  mydriatic.  A  wide  pupil  opens  up  the  passage 
for  a  larger  number  of  rays  refracted  nearer  the  periphery  of 
the  cornea,  and  in  addition  to  increasing  the  circles  of  diffusion 
in  all  meridians,  will  in  most  instances  also  increase  the  differ- 
ence in  the  refraction  in  the  two  principal  meridians.  As  a  re- 
sult of  this  the  astigmatism  as  determined  in  this  condition  will 
be  apt  to  differ  from  that  obtained  with  a  pupil  of  normal  size. 

§  74.  We  repeat  in  conclusion,  therefore,  that  what  we  wish 
to  obtain  is  the  static  refraction  of  the  eye  in  its  two  principal 
meridians  when  the  organ  is  in  its  normal  condition  and  not 
when  its  instrinsic  muscles  are  in  a  state  of  spasm  or  paralysis. 

BIBLIOGRAPHY. 


Ayres — The  use  of  atrop.  in  detenu,  glasses  and  the  influence  of  the  vasomotor  sysL 
on  the  accommod.  of  the  eye.  N.  Orl.  Med.  and  Surg.  Jr.  XI.  No,  8.  1884. 

Bjerrum,  M.  F. — Ueber  d.  Refrac.  d.  Neugeb.  Internal.  Cong,  zu  Copenhagen. 
1884. 

Bumstead,  S.  J. — The  unequal  contraction  of  the  ciliary  muscle.  Archiv.  of  Oph. 
XII.  2.  208-212. 

Dantel,  Louis — Ueber  den  Einfluss  d.  Lebensalters  auf  das  Verhalt  d.  manifst.  zur, 
totalen  Hypermetrop.  Cntbl.  f.  p.  Augenhlk.  juli-Aug.  1883. 

Dobrovolskii,  V. — Orazlichnikh  izmaineniyakh  Astig.  (some  modificats.  of  Astig). 
Voyenno  Med.  J.  III.  PL  3.  34-104.  St  Petersbg.  1868. 

Dobrowsky,  W. — Ueber  verschied.  Veranderung  d.  Astig.  unter  dem  Einfluss  d. 
Accommodat  Graefe's  Arch.  XIV.  3  Hft.  Pp.  51-105.  1868. 

Donders,  F.  C. — Ueber  scheinbare  Accommodat.  bei  Aphakie.  Graefe's  Arch. 
B.  XIX.  Abt.  I.  P.  56.  1873. 

Ely,  E,  T.— Refraction  in  the  eyes  of  newly  born  children.  Archives  of  Oph. 
VoLIX.  P.  29. 

Germann,  Theodor — Beitrage  zur  Kentniss  der  Refractionsverhaltnesse  der  kinder 
im  Sanglingsalter  sowie  im  vorshulpflichtigen  Alter.  Graefe's  Archiv.  XXXI.  2. 
Pp.  122-146. 


BIBLIOGRAPHY.  73 

Cradle,  H.— Act.  of  the  ciliary  msl.  in  astig.  Am.  J.  M.  Sc.  N.  S.  LXXVII.  Pp. 
109-11.  Phila.  1879. 

Hansen — Untersuch.  iiber  die  refract.  Verhaltnisse  in  10  bis  15  Lebensjahre  u.  das 
Wachsthum  der  Augen  in  diesen  Jahren.  Inaug.  Diss.  Kiel.  1884. 

Horstmann — Beitr.  z.  Entwickelung  d.  Refractions  verhaltnisse  d.  mensch.  Auges 
wahrend  d.  ersten  5  Lebensjahr.  Graefe's  Archiv.  1884. 

Horstmann — Refrac.  an  40  atropinozirten  Augen  von  Neugeboren.  Tagbl.  d.  53 
Vers.  Deut.  Naturfor.  u.  Arz.  zu  Danzig.  1880. 

Horstmann — Ueber  verhalt.  Refract,  v.  Kindern.  Ber.  d.  Ophth.  Ges.  zu  Heidel- 
burg.  P.  239.  1878. 

Javal,  E. — Des  variat.  de  1'astig.     Compt.  Rend,  de  la  Soc.  de  Biolog.     1873. 

Javal,  E. — Astig.  chez  les  enfts.     Gaz.  hebd.     P.  145.     1879. 

Javal,  E. — Sur  la  theorie  de  1'accommodat.  Compt.  Rend,  de  la  Soc.  de  Biolog. 
1882. 

Kaiser,  H. — Bestim.  der  sogenannten  optic.  Constant,  der  Accommodat.  u.  des 
Astig.  der  beiden  in  Betracht  gezog.  Augen.  B.  XIII.  I.  354. 

Knapp,  J.  H. — Ueber  die  Lage  u.  Kriimmung  der  Oberflachen  der  mensch.  Kris- 
tallinse  u.  den  Einfluss  ihrer  Verand  bei  der  Accommodat.  auf  die  Dioptrik  des 
Auges.  Graefe's  Arch.  B.  VI.  Abt.  II.  P.  I.  1860. 

Koenigstein — Untersuch.  an  d.  Aug.  neugeborenen  Kinder.  Wien.  Med.  Jahrbuch. 
I.  1881. 

Landesberg,  M. — Ueber  das  Auftret.  v.  regelmassig.  Astig.  bei  gewes.  Refract,  u. 
Accommodatanomal.  Graefe's  Arch.  XXVII.  Abt.  II.  Pp.  89-98.  1881. 

Pfliiger,  Dr. — Untersuchung.  der  Augen  der  Luzerner  Schuljungend.  Graefe's 
Archiv.  XXII.  4.  63-117. 

Randall,  B.  Alex. — The  refraction  of  the  human  eye.  Amer.  Jnl.  Med.  Sci.  July. 
1885. 

Reuss,  v.  A. — Beitrag  zur  Kentniss  d.  Refractverand.  im  jugendl.  Auge.  Graefe's 
Arch.  B.  XXII.  Abt.  I.  P.  210.  1876. 

Schleich — Die  Augen  von  150  Neugeborenen  oph.  untersucht.  Mitt,  aus  d.  oph. 
Klinik  zu  Tubingen.  1884.  B.  II.  H.  I. 

Ulrich,  G. — Refrac.  u.  Papilla  opt.  d.  Aug.  d.  Neugeb.  Inaug.  Dess.  Koenigsberg. 
1884. 

Unterharnscheidt — Ueber  incomplt.  oculomot.  Lahmg.  u.  accommodativ  Linsen- 
astig.  Klin.  Monatsbl.  f.  Augenhlk.  XX.  P.  37. 


CHAPTER  VI. 


OTHER   SUBJECTIVE    METHODS   OF   EXAMINATION — CHANGE   IN 

THE  FORM   OF  A  POINT  OF   LIGHT — ADAPTATION   OF 

SCHEINER'S  EXPERIMENT — THE  STENOPAIC  SLIT 

— MODIFICATIONS  OF  SNELLEN'S  FAN 

— OPTOMETERS. 

§  75.  In  view  of  the  difficulties  and  liabilities  to  error  pointed 
out  in  the  preceding  chapter,  it  is  apparent  that  there  would 
be  an  advantage  in  having  at  command  a  number  of  different 
methods  to  which  we  could  appeal  in  case  of  doubt  and  for 
verification.  Fortunately  we  are  not  without  such  resources. 

§  76.  The  various  means  used  in  the  diagnosis  of  astigma- 
tism can  be  divided  into  two  general  classes  ;  the  subjective 
and  objective. 

§77.  In  the  subjective  methods  we  rely  entirely  on  the  state- 
ment of  the  patient  as  to  how  the  test  objects  appear  and  base 
our  diagnosis  on  these  alone. 

§  78.  In  the  objective  methods  we  are  independent  of  the 
statements  of  the  patient,  and  rely  solely  on  our  own  observa- 
tions. 

§  79.  For  errors  in  the  first  method  the  patient  is  mainly 
responsible.  For  errors  in  the  second  the  observer  is  himself 
accountable. 

The  methods  described  in  Chap.  IV  belong  to  the  first 
named  class,  and  before  going  on  to  consider  those  of  the  ob- 
jective class  we  will  give  an  account  of  other  subjective  meth- 
ods which  have  been  found  useful. 

§  80.  CHANGES  IN  THE  FORM  OF  A  REMOTE  POINT  OF  LIGHT. 
— This  method,  which  was  suggested  first  by  Airy  and  was 
used  very  extensively  by  Bonders  in  the  beginning  of  his 

(74) 


KYAMINATION    WITH    A    POINT    OF    LIGHT.  75 

studies  of  astigmatism,  gives  us  directly  a  very  correct  idea  of 
the  direction  of  the  faulty  meridians.  Bonders'  plan  of  using  it 
was  as  follows  :  In  front  of  a  window-pane  of  ground  glass  he 
placed  a  black  board  abo_ut_  thirty- five  inches  square,  in  the  x  < 
middle  of  which  was  a  perforated  metallic  plate.  In  front  of 
this  perforation  can  be  brought  a  diaphragm  with  openings  vary- 
ing in  size  from  l/.2  to  10  mm.  The  patient  is  required  to  look 
at  one  of  these  openings,  having  a  diameter  of  from  2  to  4  mm.,  •*]/* 

Fig.  22. 


THE  FORM  OF  A  DISTANT  POINT  OF  LIGHT  AS  SEEN  BY  AN  ASTIGMATIC  EYE. 

at  a  distance  of  from  10  to  15  feet.  By  means  of-}-  and  — 
glasses,  if  necessary,  we  produce  alternate  M  and  H,  when  if 
there  be  any  astigmatism  present  the  point  will  be  observed  to 
be  drawn  out  in  opposite  directions  in  the  two  different 
.conditions,  indicating  the  meridians  of  greatest  and  least 
refraction. 

§8 1.  But  even  without  the  aid  of  the  spherical  lenses  it  is 
easy  to  determine  the  direction  of  the  meridians  when  astigma- 
tism is  present.  In  simple  astigmatism  either  myopic  or 
hypermetropic,  and  in  the  compound  hypermetropic  form 
the  spot  of  light  instead  of  appearing  round  and  sharply 
defined,  as  at  A,  Fig.  22,  will  appear  at  a  distance  of 
four  meters  drawn  out,  say  at  90°,  as  at  B.  In  the  simple 


76  EXAMINATION    WITH    A    POINT    OF    LIGHT. 

forms  the  ametropic  meridian  will  correspond  in  direction  with 
this,  because  while  the  rays  falling  in  the  vertical  planes  of  the 
meridian  at  180°  are  brought  to  a  focus  on  the  retina,  those 
falling  in  the  horizontal  planes,  in  meridian  90°,  unite_  either  in 
front  of  or  behind  the  retina  and  form  circles  of  diffusion  whicli 
spread  the  image  out  in  an  upward  and  downward  direction.  If 
the  round  spot  is  not  seen  clearly  at  the  usual  distance  of 
twenty  feet,  indicating  the  compound  myopic  form,  then  the 
patient  should  be  brought  nearer  until  there  is  a  distinct  elon- 
gation in  some  direction,  say  at  45°,  as  at  C,  Fig.  22.  We  then 
know  that  this  is  the  direction  of  one  faulty  meridian,  and,  of 
course,  the  other  must  be  at  right  angles  to  it. 

§  82.  But  while  this  gives  us  the  direction  of  the  principal 
meridians,  it  furnishes  no  information  as  to  the  form  of  the  astig- 
matism, the  light  spot  being  drawn  out  in  the  same  di- 
rection in  M  and  H. 

As  the  circles  of  dispersion,  however,  are  formed  in  a  differ- 
ent manner,  according  as  the  retina  lies  in  front  of  or  behind 
the  focus  of  the  refracting  media,  we  are  enabled  in  any  case 
to  determine,  in  a  very  simple  way,  to  which  category  the 
eye  belongs. 

When  the  spot  is  drawn  out  in  a  vertical  direction,  for  ex- 
ample, in  the  case  of  H,  the  dispersion  circles  are  homonymous , 
that  is  to  say,  those  belonging  to  the  upper  part  of  the  image 
are  formed  on  the  retina  above,  those  belonging  to  the  lower 
part  of  the  image,  below.  The  upper  retinal  impression  is,  un- 
der these  circumstances,  projected  downward,  and  the  lower 
one  upward.  In  the  case  of  M  we  have  an  opposite  state  of 
affairs  ;  the  upper  rays,  after  crossing,  form  circles  of  dispersion 
on  the  retina  below,  and  these  are  projected  above,  while  the 
upper  dispersion  circles  formed  by  the  lower  rays  are  pro- 
jected downward. 

When,  therefore,  a  diaphragm  is  brought  from  above 
downward  to  the  edge  of  the  pupil,  so  as  to  cut  off  the  upper 
rays  forming  the  dispersion  circles,  the  lower  portion  of  the 
diffusion  line  disappears  in  case  of  H,  and  the  upper  part  gives 
way  first  in  case  of  M.  The  same  principle  holds  good,  of 


PURVES     APPARATUS.  // 

course,  whatever  the  direction  in  which  the  spot  is  drawn  out ; 
if,  in  using  the  cutting-off  diaphragm,  the  end  of  the  line  oppo- 
site to  the  direction  from  which  it  advances  disappears  first, 
then  it  is  H ;  if  the  dispersion  circles  of  the  same  end  disap- 
pear, it  is  M. 

§  83.  Laidlaw  Purves  has  devised  a  contrivance  by  which 
the  inclination  of  the  line  can  be  determined  with  precision. 
He  draws  a  semicircle  on  the  screen  with  the  round  opening  as 
a  center,  which  is  marked  off  in  degrees.  The  degree  to  which 
the  diffusion  line  points  gives  of  course  the  direction  of  the 
meridian  that  is  at  fault.  In  order  to  facilitate  still  further 
this  reading,  he  has  a  second  screen  movable  behind  the  first, 
with  a  hole  in  it,  which  is  seen  through  a  semicircular  open- 
ing in  the  first,  made  just  below  the  semicircle  bearing  the  de- 
grees. 

To  the  astigmatic  eye  both  light  spots  appear  drawn  out  in 
the  same  direction,  and  if  the  opening  in  the  movable  diaphragm 
be  turned  until  its  diffusion  image  is  on  a  line  with  that  of 
the  center  opening,  the  degree  under  which  it  stands  marks 
the  astigmatic  meridian. 

§  84.  But  we  have  still  no  idea  of  the  degree  of  the  astig- 
matism, except  that  in  cases  where  the  dispersion  line  is  long 
we  know  that  it  is  higher  than  when  it  is  shorter.  For  its 
more  accurate  determination  we  try  cylindrical  glasses,  with 
their  axes  at  right  angles  to  the  direction  of  the  line  of  dif- 
fusion, and  when  we  find  one,  be  it  -f-  or  — ,  which  makes  the 
light  spot  again  round,  it  measures  the  degree  and  gives  us  the 
form  of  the  astigmatism. 

Snellen's  and  Dennett's  modifications  of  Stokes'  lens  are 
very  handy  for  this  purpose,  since,  by  rotating  the  disks,  we 
obtain  a  number  of  different  cylinders  in  rapid  succession. 

Purves  also  employs  this  same  method  for  determining  the 
ametropia  that  may  be  associated  with  astigmatism  in  the  com- 
pound forms.  This  he  does  by  finding  the  cylindrical  glass 
which  reduces  the  dispersion  circles  in  each  meridian  sep- 
arately. Having  this,  it  is  easy  to  find  the  ametropia  com- 
mon to  both,  and  that  which  is  in  excess  in  one  meridian. 


78  SCHEINER  S    EXPERIMENT. 

Example  : — The  spot  of  light  is  generally  diffused  in  outline, 
but  is  drawn  out  at  90°  (vertically).  A  — 2cy  axis  90°  causes  the 
lateral  dispersions  to  disappear  and  gives  the  vertical  line  sharply 
defined  edges.  The  horizontal  meridian  is,  therefore,  myopic 
2D.  With  — 3.5"7  axis  180°  the  spot  is  drawn  out  at  180°  and 
has  clean  cut  horizontal  edges.  M  in  the  vertical  meridian 
therefore  =  3.5,  and  the  case  is  one  of  comp.  myopic  astig.: 

—2  ^  —  (3-5  — 2=)  I-5cr  axis  180°. 

§  85.  Strawbridge,  of  Philadelphia,  has  also  made  a  modifi- 
cation of  this  method.  He  has  a  semicircle  of  radiating  slits 
like  Snellens'  fan  cut  in  the  diaphragm  around  the  light  spot, 
and  these  are  marked  in  degrees.  The  line  in  the  direction  of 
which  the  light  spot  in  the  center  is  drawn  out  shows  the  in- 
clination of  the  faulty  meridian. 

Fig.  23. 


SCHEINER'S  EXPERIMENT  FOR  DETERMINING  HYPERMETROPIA  AND  MYOPIA. 

§  86.  ADAPTATION  OF  SCHEINER'S  EXPERIMENT. — The  experi- 
ment first  described  by  Scheiner  is  well  known.  When  a  small 
illuminated  object — as  a  candle-flame — is  looked  at  through 
two  small  holes  in  a  diaphragm,  placed  so  close  together  that 
both  shall  fall  within  the  area  of  the  pupil,  only  one  image  is 
pictured  on  the  retina  when  it  lies  at  the  focus  of  the  refract- 
ing surfaces  of  the  eye,  as  at  E,  Fig.  23.  If  the  retina,  how- 
ever, is  found  either  in  front  of  ( H)  or  behind  ( M)  the  focus, 
two  images  are  formed,  and  two  candleflames  will  be  seen.  On 
the  distance  separating  these  two  images  and  their  relation  to 
each  other  is  based  a  diagnosis  of  the  refractive  condition  of 
the  eye. 


SCHEINER'S  EXPERIMENT.  79 

When  the  retina  lies  at  H,  images  are  formed  at  a  and  b 
and  these,  when  projected  outward,  will  be  crossed  or  heterony- 
moiis — that  is,  the  image  corresponding  to  the  upper  hole  will 
be  referred  below,  and.  that  belonging  to  the  lower  opening 
will  be  projected  upward.  When  therefore,  the  upper  hole  is 
covered  by  a  card  brought  in  front  of  it,  the  lower  candle  will 
disappear ;  and  when  the  lower  hole  is  covered,  the  upper  im- 
age will  go. 

When,  on  the  contrary,  the  retina  lies  back  of  the  focus  (M ) 
the  two  images,  a'  and  b' ,  will  be  projected  homonymously ,  and 
the  upper  image  will  correspond  to  the  upper  hole  and  the 
lower  image  to  the  lower  thole ;  and  when  the  light  coming 
through  the  upper  hole  is  cut  off,  the  upper  image  will  disap- 
pear, and  the  lower  image  will  disappear  when  the  lower  hole 
is  covered. 

The  existence  of  myopia  or  hypermetropia  can,  therefore,  be 
determined  with  great  readiness  by  simply  covering  one  of 
the  holes.  If  on  covering  the  upper  hole,  for  example,  the 
lower  candle  disappears,  there  is  hypermetropia ;  if,  on  the 
other  hand,  the  upper  candle  disappears,  there  is  myopia.  The 
distance  separating  these  images  will  furthermore  give  us  some 
idea  of  the  degree  of  ametropia ;  the  greater  the  distance  be- 
tween them,  the  greater  being  the  amount  of  myopia  or  hyper- 
metropia. The  ametropia,  however,  can  be  measured  exactly 
by  placing  in  front  of  the  holes  a  -f-  or  —  glass  which  fuses 
the  two  images.  The  number  of  this  lens  giving  the  degree 
of  M  or  If. 

§  87.  This  principle  can  be  employed  in  testing  for  astig- 
matism. Since  the  distance  between  the  two  flames  varies 
with  the  degree  of  ametropia,  when  the  holes  are  placed  suc- 
cessively before  the  different  meridians  of  the  eye  there  will 
be  a  variation  in  the  distance  between  the  images  in  case  there 
exists  a  difference  in  the  refraction  of  these  meridians.  In 
turning  the  holes  before  the  eye  one  meridian  will  be  found 
where  the  images  are  farthest  apart  and  another  where  they 
are  closest  together.  These  are  the  principal  ^meridians,  and 
the  direction  of  the  line  uniting  the  two  holes  in  these  posi- 
tions respectively,  gives  us  the  direction  of  these  meridians. 


80  THOMSON'S  APPARATUS. 

We  determine  the  form  of  the  astigmatism  in  the  same  man- 
ner as  we  do  that  of  the  general  ametropia,  by  observing 
which  flame  disappears  when  one  of  the  holes  is  covered.  If 
the  flame  on  the  same  side  disappears,  it  is  myopia,  if  the  op- 
posite one  goes,  it  is  hypermetropia.  The  degree  of  astigma- 
tism is  expressed  by  the  cylindrical  lens  which,  when  its  re- 
fracting surface  corresponds  to  the  faulty  meridian,  makes  the 
distance  between  the  images  the  same  when  the  holes  are 
brought  before  all  the  meridians. 

§88.  Thomson,  of  Philadelphia,  has  devised  a  plan  and 
invented  an  apparatus  based  on  these  phenomena,  for  the  di- 
agnosis of  the  various  forms  of  ametropia  without  the  aid  of 
glasses. 

For  this  purpose  he  employs  two  small  flames  whose  dis- 
tance from  each  other  can  be  varied.  To  the  emmetropic  eye 
these  two  flames  appear  sharply  defined  in  outline,  and  are 
united  only  when  one  passes  behind  the  other.  With  the  ame- 
tropic  observer,  however,  the  case  is  different.  To  him  each 
flame  is  an  area  of  diffused  light,  whose  extent  is  proportioned 
to  the  degree  of  his  ametropia.  In  making  an  examination,' 
the  patient  is  placed  at  a  distance  of  5  meters  from  the  two 
flames  and  they  are  gradually  approached  until  the  edges  of 
these  areas  of  diffusion  touch.  Thompson  has  calculated  the 
size  of  these  diffusion  areas  for  all  degrees  of  Ma.nd  H  for  the 
distance  of  5  meters,  and  you  read  off  on  the  arm  of  his  in- 
strument the  amount  of  departure  from  the  emmetropic  con- 
dition. In  the  instrument  he  has  described  each  space  of  2.5 
cm.  corresponds  to  one  dioptry  of  refraction. 

While  the  degree  of  the  ametropia  is  thus  arrived  at  with  tol- 
erable precision  you  have  not  as  yet  the  form.  This  you  ob- 
tain by  passing  a  card  partially  across  the  pupil,  when,  as 
explained  in  the  preceding  paragraph,  one  side  of  the  diffusion 
areas  of  both  flames  will  be  cut  off.  On  the  principle  we  have 
already  explained,  if  the  cutting  off  is  homonymous  it  is  a  case 
of  M,  if  heteronymous  it  is  H. 

In  making  use  of  these  diffusion  images  for  the  diagnosis  of 
astigmatism,  advantage  is  taken  of  the  modification  in  the  form 


THE    STENOPA1C    SLIT.  8 1 

of  the  area  of  diffusion,  as  in  Donders'  method,  and  of  the  abil- 
ity by  means  of  his  instrument  to  place  the  flames  in  a  line 
corresponding  to  any  chosen  meridian. 

In  simple  M  or  H  the  diffusion  areas  are  round,  and  when 
their  edges  are  in  contact  they  remain  so  in  whatever  meridian 
they  may  be  brought,  by  a  movement  of  the  bar  of  the  instru- 
ment. 

In  astigmatism,  on  the  other  hand,  the  diffusion  areas  are  no 
longer  round,  but  oval,  and  the  two  do  not  remain  in  contact 
when  the  arm  is  placed  in  all  meridians.  The  direction  in 
which  the  elongation  takes  place  shows  the  inclination  of  the 
principal  meridians.  The  arm  is  moved  until  the  blurred  images 
are  in  contact  at  their  shortest  diameters  and  its  inclination  to 
the  horizontal  is  noted,  and  the  amount  of  ametropia  in  that 
meridian  read  off  on  the  scale.  The  bar  is  then  turned  at  right 
angles  to  this  and  the  long  axes  of  the  images  are  brought  in 
contact.  The  position  of  the  movable  flame  on  the  scale  gives 
the  ametropia  in  this  meridian,  and  the  difference  between  the 
two  gives,  of  course,  the  amount  of  astigmatism. 

§  89.  EXAMINATION  WITH  THE  STENOPAIC  SLIT. — When  a 
diaphragm,  having  a  slit  a  millimeter  in  diameter,  is  rotated 
before  an  astigmatic  eye  looking  at  test  objects,  placed  at  a 
distance  of  5  or  6  meters,  it  will  be  found  that  when  the  slit 
corresponds  to  one  certain  meridian,  vision  is  best,  and  when  it 
is  at  the  meridian  at  right  angles  to  this  it  is  worst.  This 
gives  us  the  direction  of  the  principal  meridians,  and  we  can 
easily  find  the  refractive  condition  of  each  separately.  When 
the  slit  is  at  90°,  for  instance,  all  the  rays  which  would  pass 
through  the  other  meridians  are  cut  off  by  the  diaphragm, 
and  by  testing  in  the  usual  manner  with  -f-  and  —  spherical 
glasses  we  can  find  with  considerable  exactness  the  state  of 
refraction  of  the  meridian  open  to  the  passage  of  rays  ;  and  so 
for  any  other  meridian  whose  refraction  we  may  wish  to  deter- 
mine. 

Example  :  V  =  */36.  When  the  slit  is  at  130°  V=  */„,  when 
at  50°  it  is  less  than  */60. 

The  slit  being  at  130°,  on  trying,  in  the  usual  manner  as  de- 


82 


TEST-TYPES    OF    PRAY. 


tailed  in  Chap.  IV.,  various  spherical  glasses,  we  find  that  with 
—  1.5  V  =  */•;  therefore  meridian  130°  has  M  =  1.5.  Turn- 
ing it  now  to  50°  we  find  that  it  takes  —  4.5  to  bring  V  -  =  l/6', 

Fig.  24. 


**' 


If' 


JOS' 


30' 


"7!  O  " 

iilinll    fyfj//   '////// 


^S    KKi 


f*2 

y^w 


TEST  TYPES  BY  PRAY. 


hence  50°  has  M  =  4.5.  The  amount  of  astigmatism  is  there- 
fore 4.5  — 1.5  =  3:  But  with  this  there  is  combined  a  myopia, 
which  is  common  to  both  meridians,  of  1.5.  The  case  is  one 


CLOCK  FACE  OF  GREEN,  AND  OF  OLIVER.  83 

of  compound  myopic  astigmatism:  —  1-5  O  —  3  axis  I3°°- 
The  disadvantage  of  this  method  is  that  visual  acuteness  is  con- 
siderably reduced  by  the  exclusion  of  so  much  light  by  the 
diaphragm,  and  by  the  circles  of  dispersion,  small  it  is  true,  but 
still  appreciable,  which  come  from  the  few  rays  which  pass 
through  the  slit  in  the  other  meridian. 

§  90.  THE  TEST  LETTERS  OF  PRAY. — A  very  useful  and  con- 
venient modification  of  the  principle  of  Snellen's  fan  are  the 
test  letters  of  Orestes  Pray. 

These  letters  are  formed  by  a  series  of  parallel  lines  which 
are  inclined,  for  each  separate  letter,  at  a  different  angle  to  the 
horizontal,  as  shown,  reduced,  in  Fig.  24.  To  the  astigmatic 
eye  the  lines  composing  one  of  the  letters,  as  P  for  example, 
will  appear  most  distinct  in  outline,  while  those  of  another,  as 
B,  running  at  right  angles  to  these,  will  appear  most  indistinct. 
The  patient,  being  placed  at  such  a  distance  that  the  letters  as 
a  whole  are  distinguished  (20  feet),  is  able  to  tell  us  which  let- 
ters these  are,  and  we,  knowing  the  inclination  of  the  lines  in 
each,  are  at  once  informed  as  to  the  direction  of  the  principal 
meridians — remembering  always  that  the  most  and  least  dis- 
tinct lines  are  at  right  angles  to  their  respective  meridians. 

§  91.  John  Green,  of  St.  Louis,  devised  a  set  of  lines  drawn 
from  a  common  center  on  a  clock  face,  as  in  Fig.  25.  The  pa- 
tient indicates  the  lines  which  are  most  distinct  by  the  figure 
on  the  clock  with  which  they  correspond,  and  the  examination 
is  conducted  in  the  same  way  as  when  made  with  Snellen's  fan. 
He  has  also  designed  many  other  figures,  but  they  are  all  modi- 
ifications  of  this  general  plan,  and  are  used  in  the  same  man- 
ner. 

§  92.  Oliver,  of  Philadelphia,  has  devised  a  modification  of 
these  methods  which  consists  of  a  disk  with  three  concentric 
series  of  radiating  lines  corresponding  in  size  with  three  visual 
angles.  Two  of  Fray's  letters  are  attached  to  a  rotating  disk- 
perimeter,  one  at  an  angle  of  90°,  the  other  at  180°.  The  pa- 
tient must  designate  which  of  the  radiating  lines  he  sees  most 
distinctly.  The  disk  is  then  rotated  until  the  lines  of  one  of  the 
letters  appears  most  distinct,  which  will  mark  the  direction  of 


84 


OPTOMETERS. 


one  principal  meridian  ;  the  other  principal  meridian  will  of 
course  be  at  right  angles  to  it.  The  examination  is  then  con- 
ducted as  in  the  usual  way  with  Snellen's  fan. 

§  93.     Culbertson  has  used  the  doubling  of  an  object  when 
looked  at  through  two  prisms  with  their  bases  together  as  a 

Fig.  25. 


THE  CLOCK  FACE  OF  GREEN. 

means  of  diagnosing  ametropia.  When  the  object  is  of  a  defi- 
nite size  and  at  a  certain  distance  the  images  touch  at  their  op- 
posite edges.  The  degree  of  ametropia  is  determined  by 
the  glass,  which  when  placed  before  the  eye  gives  this  touch- 
ing for  the  standard  size  and  distance  of  the  object.  The  re- 
fraction of  the  separate  meridians  can  be  taken  by  this  means 
as  well  as  that  of  the  eye  as  a  whole. 

§94.  Nearly  all  of  the  various  optometers  can' be  used  for 
the  determination  of  astigmatism.  An  objection  to  their  use, 
however,  is  that  with  them  it  is  even  more  difficult  than  in  the 
examination  with  test-objects  at  a  distance  to  control  the  ac- 
commodation; and  to  obtain  anything  like  accurate  results  it  is 
necessary  to  paralyze  the  ciliary  muscle. 

§  95.     The  apparatus  of  Bravais,  of  Lyon,  since  it  employs  a 


ZEHENDER'S  APPARATUS.  85 

principle  somewhat  different  from  the  others,  merits  a  short 
description.  It  consists  of  a  tube  of  convenient  length,  at  one 
end  of  which  is  a  convex  lens  with  a  focal  distance  shorter  than 
the  length  of  the  tube.  The  other  end  of  the  tube  is  closed 
with  a  diaphragm  having  a  small  round  opening  in  its  center. 
The  patient  looks  through  the  tube  with  the  hole  turned  to- 
ward a  lamp  or  window,  and  if  astigmatism  be  present  the  round 
light  spot  will  appear  oval  as  in  Bonder's  experiment  (§81) 
with  its  long  diameter  in  the  direction  of  the  most  strongly  re- 
fracting meridian.  In  the  interior  of  the  tube  there  is  another 
spherical  lens  which  can  be  rotated  on  its  axis  in  any  desired 
meridian,  and  thus  made  to  act  as  a  cylinder  (see  §  25).  An 
index  on  the  outside  shows  the  degree  of  inclination  of  this 
lens  when  the  light  spot  again  becomes  round,  and  a  table 
shows  the  number  of  the  cylinder  to  which  this  inclination  cor- 
responds. 

§  96.  Zehender  has  adapted  the  method  first  employed  by 
Young  into  the  form  of  an  instrument  which  he  uses  for  esti- 
mating the  degree  of  astigmatism  and  the  direction  of  the  prin- 
cipal meridians.  He  has  a  few  fine  threads  stretched  parallel 
to  each  other  across  one  end  of  each  of  two  tubes,  one  of  which 
is  inserted,  telescope  fashion,  into  the  other.  When  the  tubes 
are  so  placed  that  the  threads  of  one  lie  close  against  and  at 
right  angles  to  the  other,a  non-astigmatic  eye  sees  them  all  with 
equal  distinctness  when  the  tubes  are  rotated  to  any  position 
on  their  common  axis.  When  the  inner  tube  is  withdrawn, 
separating  the  two  bands  of  threads  to  any  considerable  distance, 
however,  it  is  no  longer  possible  for  the  eye  not  astigmatic  to 
see  both  bands  distinctly  at  the  same  time.  When  the  eye  is 
astigmatic  this,  of  course,  is  not  always  true.  When  the  bands 
are  at  right  angles  and  the  tubes  are  revolved  on  their  long  axis 
there  is  one  position  in  which  the  threads  of  one  band  are 
seen  clearest  and  those  in  the  other  least  so.  The  bands 
then  lie  in  the  direction  of  the  principal  meridians.  Spherical 
glasses  are  now  placed  before  the  eye,  one  after  another,  until 
one  is  found  which  brings  out  the  indistinct  band  clearly. 
The  number  of  this  glass  expresses  the  amount  of  astigma- 


86  JAVAL'S  ASTIGMOMETER. 

tism  in  the  meridian  at  right  angles  to  the  direction  of  the 
band. 

§97.  Javal's  Astigmometer : — As  stated  in  §  94,  one  of 
the  principal  defects  inherent  in  all  the  methods  of  opto- 
metric  measurement  where  the  test  object  is  within  a 
finite  distance  and  close  to  the  eye,  is  the  almost  unavoidable 
tendency  to  the  use  of  the  accommodation.  We  have  always 
been  accustomed  to  use  the  accommodation  when  the  object 
is  near  us  and  when  we  know  that  it  is  at  the  other  end  of  a 
short  tube  we  instinctively  accommodate  for  that  distance. 

When  the  visual  axes  are  parallel,  however,  as  when  we  look 
at  infinity,  the  ciliary  muscle  is  usually  relaxed.  Javal  has 
taken  advantage  of  this  fact  in  the  construction  of  his  astigmo- 
meter. 

As  a  test  object  he  uses  a  circle  with  lines  drawn  through  its 
center  at  every  15  degrees.  This  circle  is  looked  at  through 
a  convex  lens  having  a  focus  of  about  five  inches.  To  the  eye 
free  from  astigmatism,  of  course,  all  the  lines  appear  of  the 
same  distinctness.  The  astigmatic  eye  sees  some  more  clearly 
than  others,  and  the  card  on  which  the  circle  is  drawn  is  moved 
back  and  forth  until  one  line  becomes  sharply  defined.  This 
line  will  lie  in  the  direction  of  the  meridian  of  greatest  refrac- 
tion. Concave  cylindrical  lenses  are  then  placed  successively 
before  the  eye,  beginning  with  the  weakest,  with  their  axes  at 
right  angles  to  the  distinct  line  until  one  is  found  through 
which  all  the  lines  appear  with  uniform  sharpness  of  outline. 
We  thus  obtain  the  direction  of  the  principal  meridians  and 
the  degree  of  astigmatism.  The  ametropia  that  may  be  asso- 
ciated with  the  astigmatism  is  determined  subsequently.  In 
order  to  avoid  any  interference  on  the  part  of  tfie"  accommoda- 
tion, he  has  a  second  circle  drawn  on  the  card,  with  its  center 
at  the  same  distance  from  the  center  of  the  circle  with  the  lines 
as  separates  the  visual  axes  of  the  eyes  in  a  state  of  parallelism. 
When  the  two  eyes  look  at  these  circles,  therefore,  there  will 
be  two  circles  seen  unless  the  visual  axes  are  parallel.  'When 
the  patient  sees  only  one  circle  with  both  eyes  open,  the  eyes 
are  adapted  for  distant  vision  and  the  accommodation  is  re- 
laxed. 


BIBLIOGRAPHY. 


BIBLIOGRAPHY. 


Anderson,  T. — New  instrument  for  estimat.  astig.     Lancet.     II.     P.  415.     1880. 

Bravais — Nouv.  appareil  pour  diagnost.  1'astig.  Lyon  Med.  X.  Pp.  478-81. 
1872. 

Culbertson,  H. — A  method  of  determ.  ametropia  by  prism,  refraction.  Cincin. 
Lancet  and  Clinic.  X.  P.  49.  1883. 

Farley,  C.  H. — A  method  of  discover,  and  correct,  astig.  Bost.  M.  and  S.  J. 
LXXXVI.  Pp.  381-3.  1872. 

Gavarret — Astig.  optometre  de  M.  Javal.  Gaz.  d'Hop.  XL.  P.  326.  Paris. 
1867. 

Green,  J. — On  the  detect,  and  measurement  of  astig.  Am.  J.  M.  Sc.  n.  s.  LIII. 
Pp.  117-27.  1867. 

Green,  J.— On  a  color-test  for  astig.    Trs.  Amer.  Ophth.  Soc.  N.  Y.  P.  130.  IV-V. 

Green,  J. — On  an  optic,  demonstrat.  of  the  characterist.  phenom.  of  astig.  vis.,  by 
the  cam.  obscur.  and  by  the  magic  lantern.  St.  Louis  M.  and  S.  Jr.  N.  S.  V.  Pp. 
107-9.  l868- 

Green,  J. — An  optic,  demonstrat.  of  the  character,  phenom.  of  astig.  vis;  Trs.  M. 
Ass.  Mo.  1869.  Pp.  170-81.  St.  Louis.  1870. 

Green,  J. — On  a  new  syst.  of  tests  for  the  detect  and  measur.  of  astig.,  with  an 
analys.  of  64  cases  of  refract,  anomal.  obsd.  by  the  aid  of  this  method.  Trs.  Am. 
Ophth.  Soc.  Pp.  13—43.  Tr.  Am.  Ophth.  Soc.  N.  Y.  1867-8.  IV-V.  1869. 

Green,  J. — Test-diagrams  for  the  detect,  and  measur.  of  astig.  Trs.  Am.  Ophth. 
Soc.  1878. 

Heymann — Astig.    Tafeln  nach    Dr.  Pray.      (2  Tafeln).     Leipzig.    Engelmann. 

Javal,  E. — Ueber  ein  neues  Instrmt.  zur  Prtifg.  des  Astig.  Klin.  Monatsbl.  f. 
Augenhlk.  P.  334.  1865. 

Javal,  E.  Sur  un  nouvl.  instrmt  pour  la  determinat.  de  1'astig.  Ann.  d'oculist. 
T.  LVII.  P.  39.  1867. 

Javal,  E. — Sur  les  applicat  d'un  appareil  nouveau  destine  a  determ.  1'astig.  visuel. 
Bull.  Soc.  d'anthrop.  de  Paris.  2  S.  XII.  Pp.  149-58.  1877. 

Morosini,  D. — Determinaz.  di  miop.,  ipermetrop.  astig.     Sassari.     1833. 

Laidlaw  Purves.  Eine  Methd.  z.  Bestim.  der  Refrctanoml.  Graefes  Arch.  B. 
XIX.  Abt.  I.  P.  89.  1873. 

Oliver,  C.  A. — Descript.  of  a  rotat.  disc  for  test,  for  astig.    Med.  News,  Oct.  6, 1883. 

Pray,  O.  M.— Test-type  for  astig.  Arch.  Ophth.  and  Otol.  N.Y.  I.  No.  I.  Pp. 
17-21.  1869. 

Prouff,  J.  M. — De  la  sclerotoscopie.  Methd.  a  suivre  pour  les  observat.  ayant  trait 
a  la  "keratite"  pretendue  "astig."  Rev.  clin.  d'oculist.  No.  2.  P.  25.  1884. 

Schoen — Apparat  z.  Bestim.  d.  Astig.  besonders  in  seitlch.  Sehrichtungen 
Graefes  Arch.  XXIV.  Abt.  I.  P.  91.  1878. 

Strawbridge,  G. — An  addit.  method  for  the  determ.  of  Astig.  Trs.  Am.  Ophth. 
Soc.  VIII.  Pp.  100-4.  N.  Y.  1871. 

Thomson,  W. — Determinat.  of  degree  of  ametp.  Am.  J.  M.  Sc.  Pp.  414-20. 
1870. 

Thomson,  W. — A  pract.and  rapid  method  with  an  instr.  for  the  diag.  of  the  refract. 
Trs.  Amer.  Oph.  Soc.  V.  II.  Part  4. 


88  BIBLIOGRAPHY. 

Thomson,  W. — An  addit  test  for  the  diag.  and  correct  for  the  optic,  defects  of  the 
eye.  Am.  J.  M.  Sc.  P.  76.  1870, 

Tweedy,  J. — On  an  improved  optometer  for  estim.  the  degree  of  abnorm.  reg.  astig. 
London  Lancet  II.  Pp.  604-6.  1876. 

Zehender;  W. — Ueber  die  Brewster.  rnethd.  z.  Bestim.  der  Brechungsexponenten 
flUssigoder  fetweich.  Substanzen.  Graefes  Arch.  B.  III.  Abt  I.  P.  99.  1857. 

Zehender,  W. — Zur  Astigmonietrie.  Bercht  a.  d.  15  versam.  d.  ophth.  Gesellsch. 
P.  29.  1883. 

Weil,  J. — Essai  sur  la  determ.  cliniq.  de  1'astig.  4°.     Paris.     1875. 


CHAPTER   VII. 


OBJECTIVE  METHODS  OF  EXAMINATION — THE  OPHTHALMOSCOPE 
AS  A  MEANS  OF  DIAGNOSIS  IN  ASTIGMATISM. 

§  98.  In  the  objective  methods  of  examining  for  astigma- 
tism we  do  not  rely,  as  in  the  subjective  methods  just  de- 
scribed, on  the  statements  of  the  patients  for  the  data  of  diag- 
nosis, but  trust  entirely  to  our  own  observations.  The  ad- 
vantage of  the  plan  is  very  great,  since  it  makes  us  indepen- 
dent of  the  patient,  and  eliminates  the  most  potent  sources  of 
error.  For  a  satisfactory  examination  by  the  subjective  meth- 
ods a  certain — in  fact  a  very  considerable — amount  of  intelli- 
gence on  the  part  of  the  patient  is  necessary.  This,  unfortu- 
nately, on  account  of  age  or  mental  condition,  we  do  not  al- 
ways have  at  command,  and  had  we  not  some  other  means  of 
getting  at  the  facts  it  would  be  often  impossible  to  arrive  at 
any  intelligent  or  definite  idea  as  to  the  refractive  state  of  the 
eye. 

The  special  advantages,  as  well  as  the  defects  and  short- 
comings of  the  various  objective  modes  of  examination,  will  be 
pointed  out  when  we  come  to  a  consideration  of  each  plan  in 
detail. 

§  99.  THE  OPHTHALMOSCOPE  IN  THE  DIAGNOSIS  OF  ASTIG 
MATISM. — When  Helmholtz  invented  the  ophthalmoscope  he 
not  only  gave  to  the  profession  an  instrument  by  means  of 
which  the  condition  of  the  interior  of  the  eye  could  be  exam- 
ined in  minutest  detail,  but,  what  is  hardly  less  valuable,  put 
into  their  hands  an  apparatus  for  testing  its  optical  state. 

The  ophthalmoscpe,  as  an  optometer,  has  now,  become  one 
of  our  most  important  and  reliable  means  of  diagnosis. 

§  IOO.  There  are  two  ways  of  making  an  examination  with 
the  ophthalmoscope.  One  is  the  direct  method,  giving  an 

(89) 


90  DIRECT  METHOD  OF  EXAMINATION. 

erect  and  virtual  image  of  the  fundus  of  the  eye ;  the  other  is 
the  indirect  method,  in  which  the  image  of  the  fundus  is  in- 
verted and  actual.  The  manner  in  which  these  two  kinds  of 
images  are  obtained  is  essentially  different  in  the  two  methods. 

For  the  fundamental  principles  of  ophthalmoscopy  we  shall 
have  to  refer  the  reader  to  general  treatises  on  the  subject. 

§  101.  The  Direct  Method  of  Examination. — In  this  method 
we  look  directly  into  the  eye  to  be  examined  and  see  the  fun- 
dus in  its  proper  position,  but  under  the  magnifying  power 
of  its  refracting  media. 

It  will  simplify  our  study  somewhat  if  we  remember  that 
when  we  employ  the  ophthalmoscope  as  an  optometer  in  ame- 
tropia,  we  are  only  using  one  optical  instrument  to  neutralize 
the  action  of  another,  in  the  same  way  as  we  determine  the 
strength  of  a  +  lens  by  the  —  lens  necessary  to  overcome  its 
refraction  and  reduce  its  optical  properties  to  zero. 

As  in  the  determination  of  general  ametropia  by  glasses,  it 
is  the  object  to  so  alter  the  course  of  parallel  rays  that  they 
may  appear  to  come  from  the  far  point  of  the  eye  under  ex- 
amination, so,  in  making  a  diagnosis  with  the  ophthalmoscope 
by  the  direct  method,  it  is  the  purpose  to  render  the  rays  which 
come  out  of  the  ametropic  eye,  and  are  directed  to  its  far 
point,  parallel.  In  both  cases  the  glass  which  does  this  gives 
the  amount  of  deviation  of  the  eye  from  the  emmetropic  con- 
dition. 

§  IO2.  This  principle,  as  applied  to  the  direct  method  of 
ophthalmoscopy,  is  shown  in  Fig.  26.  The  eye  V  is  myopic, 
and  the  rays  e  f  coming  from  a  point  o  of  the  illuminated 
fundus,  after  passing  out  of  the  eye  converge  towards  its  far- 
point  situated  at  a,  six  inches  in  front  of  the  cornea.  The  eye 
E  of  the  emmetropic  observer  is  not  adapted  for  converging 
rays,  and  in  order  to  have  the  rays  e  f  brought  to  a  focus 
on  his  retina  they  must  be  rendered  parallel.  This  can  be 
done  by  placing  a  concave  lens  having  a  negative  focus  of  five 
inches  behind  the  ophthalmoscopic  mirror  and  one  inch  in 
front  of  the  eye  to  be  examined.  The  rays  e  f  directed  to  the 
negative  focus  of  the  lens,  also  at  a,  will  then  be  made  parallel, 


DIRECT  METHOD  OF  EXAMINATION.  9 1 

and  the  emmetropic  eye  E  being  in  a  state  of  repose  and 
adapted  for  parallel  rays,  will  unite  them  on  its  retina,  and 
they  will  form  there  a  clear  and  distinct  image  of  the  point  o. 
This  same  lens,  acting  in  a  contrary  sense,  will  render  parallel 
rays  coming  from  distant  objects  divergent  as  though  they 

Fig.  26. 


DIRECT  METHOD  OF  EXAMINATION  WITH  THE  OPHTHALMOSCOPE. — Alteration  in 
the  course  of  the  rays  by  concave  lenses  in  the  principal  meridians  in  compound  my- 
opic astigmatism. 

came  from  the  point  a,  five  inches  in  front  of  it  (that  is  the  far- 
point  of  the  eye).  Therefore,  the  same  concave  lens  through 
which  an  emmetropic  observer  can  see  the  fundus  of  a  myopic 
eye  distinctly  expresses  the  degree  of  myopia  of  the  observed 
eye,  and  will  adapt  it  to  vision  at  an  infinite  distance. 

In  the  example  we  have  taken  the  rays  ef  belong  to  one  merid- 
ian— the  vertical — but  if  the  refracting  surfaces  are  the  same  in 
all  meridians,  as  in  ordinary  simple  myopia,  the  law  applies 
to  the  others  as  well,  and  through  all  points  situated  in  every 
meridian  there  will  proceed  rays  convergent  towards  a  which 
which  will  be  rendered  parallel  by  the  same  lens  ( — 1/5)  and  be 
again  united  on  the  retina  of  E.  Under  these  conditions, 


92  DIRECT  METHOD  IN  DIAGNOSING  ASTIGMATISM. 

therefore,  the  emmetropic  observer  E  will  be  able  to  see  with 
distinctness  all  the  details  at  the  fundus  of  V,  and  the  fine 
retinal  vessels  running  in  one  direction  will  be  made  out  as 
clearly  as  those  running  in  any  other. 

§103.  The  state  of  affairs  is  very  different,  however,  when 
we  come  to  deal  with  an  eye  having  a  different  curvature  in 
each  meridian,  as  in  regular  astigmatism. 

Here  the  far-point  to  which  the  emerging  rays  converge,  in 
the  case  of  compound  myopic  astigmatism,  will  be  in  a  differ- 
ent position  for  the  two  principal  meridians, being  nearest  to  the 
eye  in  the  most  strongly  refracting,  and  farthest  from  it  in  the 
weakest.  Letting  V  and  H,  Fig.  26,  represent  the  two  meri- 
dians of  greatest  and  least  refraction  respectively,  a  will  be 
the  far  point  of  V,  6  inches  in  front  of  the  cornea,  and  b  that 
of  H,  9  inches  in  front  of  the  cornea.  It  would  not  be  possi- 
ble, therefore,  for  any  one  spherical  lens  to  render  the  rays 
coming  through  these  two  meridians  parallel  so  that  they 
would  be  united  at  the  same  place  on  the  retina  of  E,  and  as  a 
consequence  the  observer  could  never  obtain,  by  such  a  lens,  a 
uniformly  distinct  image  of  the  details  of  the  fundus.  If  the 
delicate  vessels  running  in  the  vertical  direction  were  seen 
sharply  with  —  l/Bt  those  running  in  the  horizontal  direction 
and  corresponding  to  the  opposite  meridian,  V,  would  be 
blurred.  When,  on  the  other  hand,  a  —  l/6  lens  is  used  which 
renders  the  fine  vessels,  running  horizontally  and  correspond- 
ing to  the  vertical  meridian  V,  sharply  defined,  those  running 
in  the  opposite  direction  are  indistinct. 

§  104.  On  this  principle  and  in  consonance  with  these  facts 
is  based  one  of  the  methods  of  diagnosing  astigmatism  by  means 
of  the  ophthalmoscope. 

The  refraction  of  each  principal  meridian  is  taken  separately, 
just  as  if  it  were  a  case  of  simple  ametropia.  The  mirror  of 
a  refraction  ophthalmoscope  is  brought  close  to  the  observed 
eye  and  the  disk  containing  the  correcting  lenses  is  turned  un- 
til one  lens  is  found  through  which  the  finest  retinal  vessels 
running  in  one  direction  appear  sharply  defined.  Let  us  say, 
for  example,  that  the  delicate  vessels  running  horizontally  over 


DIRECT  METHOD  IN  DIAGNOSING  ASTIGMATISM.  93 

the  outer  edge  of  the  optic  disk  are  clearly  made  out  with  —  3. 
The  fine  vessels  running  almost  vertically  in  the  region  of  the 
macula  lutea  will,  through  the  same  lens  appear  blurred  and  in- 
distinct (the  accommodation  of  the  observer  remaining,  of 
course,  in  a  state  of  complete  relaxation).  The  converging 
rays  coming  from  these  horizontal  vessels  and  passing  through 
the  vertical  meridian  of  the  eye  are  rendered  parallel  by  the 

—  3  and  thus  become  adapted  to  the  emmetropic    observer. 
The  vertical  meridian  has  therefore  M  =  3.     The  small  verti- 
cal vessels  near  the  macula  are  seen  distinctly  with  —  I,  while, 
with  the  same  lens,  the  horizontal  vessels  at  the  edge  of  the 
disc  appear  blurred.     The  horizontal  meridian  which  refracts 
the  rays  coming  from  these  vertical  vessels  is  myopic  to  the 
extent  of  I  D.     The  case  is  one  of  Comp.  My.  Astig.  —   J   O 

—  2  axis  1 80°.     The   same  principle  applies,  of  course,  to  all 
the  other  forms  of  astigmatism.     The  direction   of  the  vessels 
which  are  seen  most  distinctly  gives  the  direction  of  the  prin- 
cipal meridians,  and  the  lenses  +,or  — ,through  which  they  are 
thus  seen  gives  the  degree   of  ametropia  for  each  respectively. 
The  degree  of  astigmatism  is  expressed  by  the  difference  in 
the  refraction  of  the  opposing  meridians. 

§  105.  The  defects  of  this  method  are  two.  There  is,  first, 
the  impossibility  of  determining  in  all  cases  the  exact  direction 
of  the  faulty  meridians.  The  fine  vessels  of  the  retina  which 
we  employ  as  test-objects  do  not  spread  out  regularly  in  all  di- 
rections like  a  Snellen's  fan,  and  frequently  there  is  no  one 
which  follows  the  exact  line  of  the  axis  of  either  one  of  the 
principal  meridians.  Our  estimate  of  the  direction  of  the  me- 
ridians is,  therefore,  only  approximative,  and  cannot  be  made 
certain,  except  by  some  one  of  the  other  methods.  Neverthe- 
less, we  can  always  obtain  an  idea  of  their  general  direction, 
and  this  is  frequently  of  the  utmost  importance  as  furnishing  a 
key  to  the  situation. 

The  second  defect  applies  equally  to  the  determination 
of  general  ametropia  by  this  means,  and  that  is  the  want  of  ex- 
actness in  estimating  the  degree  of  ametropia  in  each  meridian. 
My  observations  and  experience  as  a  teacher  have  convinced 


94  LIMITATIONS  OF  THE  METHOD. 

me,  that  it  is  not  given  to  all  men  to  be  good  ophthalmoscop- 
ists.  particularly  by  the  direct  method.  A  perfect  result  in  de- 
termining refraction  in  this  way  requires,  in  the  first  place,  an 
absolute  control  over  the  accommodation  on  the  part  of  the 
observer,  and  this  cannot  be  acquired  by  every  one.  A  very 
slight  change,  one  of  which  we  are  not  at  all  conscious,  in  the 
tension  of  the  ciliary  muscle  will  make  a  difference  of  0.5  or 
0.75  D.  Then,  again,  if  the  media  are  not  quite  clear  and  the 
pupil  is  small,  as  we  have  it  nearly  always  in  advanced  life,  it  is 
not  possible  to  distinguish  within  0.75  D,  between  the  lenses 
which  give  the  clearest  outline  to  a  particular  vessel.  It  is  to 
be  remembered,  also,  that  particularly  in  M,  the  vessels  which 
serve  us  as  test-objects  are  not  all  on  the  same  level.  Those  at 
the  edge  of  the  disc  are  in  advance  of  those  at  the  macula,  and 
it  is  the  refraction  of  the  meridians  at  the  latter  place  we  want. 
Where  the  pupil  is  so  small  as  to  seriously  diminish  the  illumi- 
nation of  the  fundus,  a  mydriatic  should  be  used.  Of  these, 
hydrochlorate  of  cocaine  and  hydrochlorate  of  homatropine  are 
best,  since  their  effect  on  the  accommodation  is  more  transient 
than  that  of  atropine. 

While  acknowledging  that  there  are  some  brilliant  excep- 
tions to  the  general  rule,  I  yet  believe  that,  taking  ophthalmo- 
scopic  observers  in  the  mass,  it  is  not  possible  in  an  average  of 
cases,  to  determine  within  0.75  D  of  the  actual  refractive  condi- 
tion of  the  eye,  by  means  of  the  ophthalmoscope. 

But  notwithstanding  this,  ophthalmoscopic  examination  by 
the  direct  method  is,  and  will  probably  always  remain,  one  of 
our  readiest  and  most  reliable  aids  in  the  diagnosis  of  astigma- 
tism ;  and  all  students  of  ophthalmoscopy  should  diligently 
practice  the  method  and  endeavor  to  acquire  the  greatest 
amount  of  skill  possible  in  its  use. 

§  1 06.  The  general  appearance  of  the  fundus  of  the  astigma- 
tic eye  is  very  striking,  particularly  in  the  high  degrees  of  the 
anomaly  and,  when  once  seen  and  understood,  is  not  likely 
thereafter  to  be  mistaken  for  anything  else.  With  the  excep- 
tion of  keratometry,  to  be  considered  later,  I  know  of  no  other 
method  which  gives  us  so  promptly  such  important  informa- 


INACCURATE  REPRESENTATIONS  OF  THE  ASTIGMATIC  FUNDUS.        95, 

tion  as  to  the  existence  of  these  high  degrees  of  astigmatism 
which  are  so  puzzling  when  tested  by  the  subjective  methods 
alone.  A  single  glance  is  often  sufficient  to  reveal  to  us  the 
direction  of  the  principal  meridians,  and  furnish  an  indication 
as  to  the  special  form  of  the  anomaly. 

Fig.  27. 


DIAGRAM  REPRESENTING  JAEGER'S  INACCURATE  DRAWING  OF  THE  FUNDUS  OF  THE. 
ASTIGMATIC  EYE  AS  SEEN  BY  THE  DIRECT  METHOD. 

There  does  not  exist,  to  my  knowledge,  a  drawing  represent- 
ing the  fundusof  the  astigmatic  eye  with  any  approach  to  faith- 
fulness. Jager  has  in  his  well-known  atlas  (Fig.  31  of  the 
smaller  edition),  a, drawing  which  purports  to  give  the  appear- 
ance of  the  fundus  as  seen  in  the  direct  method,but  it  is  far  from 
a  true  picture.  That  so  faithful  a  delineator  as  Jager  should  com. 
mit  such  an  error  is  indeed  wonderful.1  Fig.  27  is  a  diagrammatic 

1  In  Loring's  text-book  of  ophthalmoscopy  which  has  appeared  since  the  MS.  of 
this  chapter  has  been  in  the  hands  of  the  printer,  there  is  a  representation  of  the  fun- 
dus of  the  astigmatic  eye.  While  more  nearly  accurate  than  Jager's,  it  yet  fails  to- 
give  that  marked  contrast  which  exists  between  the  distinctness  of  the  vertical  and 
horizontal  vessels. 


96  APPEARANCE  OF  THE  FUNDUS  IN  ASTIGMATISM. 

copy  of  this  drawing  and  a  glance  at  it  will  show  that  it  could  not 
by  any  possibility  be  the  fundus  of  an  eye  as  seen  through  an 
astigmatic  refracting  system.  The  fine  retinal  vessels  are  seen 
running  in  all  directions  with  equal  distinctness  which,  as  we 
have  shown,  could  not  be  the  case  in  an  astigmatic  eye.  The 
only  part  of  the  drawing  which  has  any  semblance  of  truth  is 
the  appearance  of  the  optic  disk.  This  does  give  a  very  good 
picture  of  the  disk  as  it  appears  when  the  meridian  is  adapted 
to  the  eye  of  the  observer.  The  vertical  outlines  are  sharp, 
while  the  horizontal  outlines  are  blurred  and  indistinct.  But 
under  the  optical  conditions  producing  this  effect  it  would  not 
be  possible  to  see  the  delicate  retinal  vessels  running  horizon- 
tally over  the  edge  of  the  disk  as  they  are  represented  in 
Jager's  figure.  So  far  as  I  know  attention  has  not  before  been 
called  to  the  falseness  of  this  representation.  Even  so  good 
and  able  an  observer  as  Nettleship  has  copied  it  into  his  text- 
book without  any  allusion  to  its  inaccuracy. 

I  have  endeavored  to  give  in  Fig.  28  a  more  nearly  accurate 
representation  of  the  appearance  of  the  fundus  of  an  astig- 
matic eye  when  examined  by  the  direct  method.  It  was 
sketched  from  a  case  of  simple  myopic  astigmatism  of  6  D 
axis  1 80°,  and  it  is  given  as  seen  without  any  correcting  lens. 

The  horizontal  meridian  being  emmetropic,  and  the  eye  of 
the  observer  being  emmetropic  also,  the  parallel  rays  which 
pass  out  through  this  meridian  are  focused  properly  on  the 
retina  of  the  observer,  and  consequently  all  vertical  outlines 
are  distinct.  The  large  retinal  vessels  passing  upward  and 
.  downward  over  the  face  of  the  disk  are  seen  sharply  defined 
with  the  light  reflex  along  their  center  very  clear.  As  soon, 
however,  as  the  vessels  become  defle*cted  to  one  side  and  as- 
sume an  oblique  or  horizontal  direction  out  of  the  axis  of  the 
emmetropic  meridian  their  outlines  become  blurred,  the  reflex 
is  lost,  and  their  course  is  marked  only  by  an  ill-defined  band 
whose  outlines  merge  into  the  surrounding  red  of  the  fundus. 
Wherever  in  their  course,  they  again  assume  a  vertical  direc- 
tion, their  outlines  become  once  more  sharply  defined;  all  light 
points  are  converted  into  vertical  light  lines,  and  all  black 

-       .'"'i   ";•       s^ALr 


APPEARANCE    OF    THE    FUNDUS    IN    ASTIGMATISM.  9/ 

points  or  masses  become  vertical  black  lines,  giving  the  fundus 
a  striking  appearance  of  vertical  "  streakiness."  The  vertical 
sides  of  the  optic  disk  are  sharp  in  outline  while  superiorly 
and  inferiorly  they  are  "fuzzy"  and  indistinct,  and,  as  a 
whole,  the  disk  appears  vertically  elongated.  Such  an  ap- 

Fig,  28. 


APPEARANCE  OF  THE  FUNDUS  OF  AN  ASTIGMATIC  EYE  AS  SEEN  BY  THE  DIRECT 
METHOD  OF  EXAMINATION. 

pearance  could  easily  be  mistaken  by  a  novice  for  a  patho- 
logical condition — a  retinitis  or  neuro-retinitis.  I  distinctly 
remember  in  my  first  workings  with  the  ophthalmoscope,  be- 
fore I  had  studied  astigmatism,  making  such  an  error  in  diag- 
nosis, which  was,  however,  promptly  corrected  by  one  whose 
experience  in  such  matters  was  greater  than  mine. 


98  APPEARANCE    OF   THE    FUNDUS    IN    ASTIGMATISM. 

A  very  good  idea  of  these  appearnces  may  be  obtained  by 
looking  at  a  drawing  of  a  normal  fundus  in  any  ophthahno- 
logical  atlas  through  a  -f  cylindrical  lens  of  six  inches  focus 
placed  with  its  axis  vertical,  close  to  the  eye  and  at  six  inches 
from  the  drawing.  If  the  accommodation  of  the  observer  is 
then  relaxed  the  rays  coming  from  the  vertical  vessels  and 
passing  through  the  horizontal  meridian  will  be  rendered  par- 
allel by  the  lens,  focused  by  the  observing  eye  on  its  retina, 
and  seen  clearly,  while  the  others,  coming  from  the  horizontal 
and  oblique  lines  and  passing  through  the  other  meridians 
will  unite,  if  at  all,  behind  the  retina,  and  give  images  with 
blurred  outlines. 

§  107.  The  same  principles  apply,  of  course,  to  every  form 
of  astigmatism  with  the  principal  meridians  lying  in  all  possi- 
ble directions.  If,  in  the  case  taken  as  an  example,  the  my- 
opia of  the  vertical  meridian  is  corrected  by  a  —  6  spherical 
behind  the  ophthalmoscopic  mirror,  rendering  the  horizontal 
meridian  hypermetropic,  the  horizontal  vessels  will  come  out 
clear  and  distinct,  and  all  the  vessels  running  vertically  will 
appear  blurred,  since  the  rays  coming  from  them  cross  behind 
the  retina,  while  the  disk  will  seem  to  be  drawn  out  horizon- 
tally, with  its  superior  and  inferior  borders  sharply  defined.  If 
the  meridians  are  oblique,  the  disk  will  be  elongated  in  corre- 
sponding directions  when  the  ametropia  of  each  is  corrected, 
and  those  portions  of  the  vessels  which  run  in  these  direc- 
tions will  be  sharply  outlined. 

§  108.  In  examining  for  ametropia  by  the  direct  method 
care  should  be  taken  to  so  arrange  the  relative  position  of  the 
head  of  the  patient  to  the  light  that  the  ophthalmoscope  shall 
be  as  nearly  as  possible  at  right  angles  to  the  optical  axis  of 
the  eye  under  examination.  If  this  precaution  be  not  taken 
and  the  correcting  glass  behind  the  mirror  is  inclined  to  the 
direction  of  the  rays  coming  from  the  eye,  there  will  be  a  cyl- 
indrical action  on  the  part  of  the  lens,  as  demonstrated  in  §  25. 
It  was  for  the  purpose  of  obviating  this  source  of  error,  among 
others,  that  the  various  "  tilting "  ophthalmoscopic  mirrors 
were  invented,  (Loring,  Wadsworth,  DeWecker,  and  others). 


OPHTHALMOSCOPES    WITH    CYLINDRICAL   ATTACHMENTS.        99 

§  109.  Dennett,  Uhtoff  and  Parent  have  described  modifi- 
cations of  the  refraction  ophthalmoscope  by  which  it  is  possi- 
ble to  examine  the  fundus  of  the  astigmatic  eye  through  cor- 
recting cylinders. 

Uhtoff 's  (Shoeler's)  instrument  consists  of  a  disk  with  ten 
cylinders  (-)-  and  — )  which  is  fixed  to  one  side  of  the  instru- 
ment back  of  the  mirror,  the  disk  containing  the  sphericals 
being  fastened  at  the  other  side.  The  glasses  contained  in 
these  disks  can  be  brought  by  rotation,  as  in  the  ordinary  in- 
struments, behind  the  perforation  in  the  mirror,  superposed  if 
necessary.  The  disk  containing  the  cylinders  can,  in  addition, 
be  so  turned,  as  a  whole,  that  the  axis  of  the  cylinder  behind 
the  perforation  can  be  placed  in  any  desired  direction. 

Parent's  instrument  is  constructed  on  the  same  principle. 

Dennett  used  a  small  Stokes'  lens  behind  the  opening  in 
the  mirror.  He  tells  me,  however,  that  he  has  ceased  to  use 
it  for  some  time. 

Such  instruments  I  do  not  consider  of  any  great  value  for 
making  a  first  diagnosis  of  astigmatism,  for  there  are  many 
other  means  easier  and  more  ready  and  reliable.  It  is,  how- 
ever, often  of  great  importance  to  be  able  to  examine  in  detail 
the  fundus  of  an  astigmatic  eye,  to  determine  the  presence  or 
absence  of  pathological  changes  there.  In  an  eye  even  mod- 
erately astigmatic  this  is  not  possible  by  the  direct  method. 
Some  means  by  which  this  can  be  done  is,  therefore,  im- 
perative. 

The  instruments  above  mentioned  would  enable  us  to  do 
this,  but  they  are  more  or  less  cumbersome  and  somewhat 
expensive.  It  occurred  to  me,  therefore,  that  some  modifica- 
tion of  the  ordinary  ophthalmoscope  was  possible  which  would 
enable  us  to  use  for  this  purpose  the  cylindrical  glasses  in  our 
cases  of  test  lenses.  Such  a  modification  I  have  devised,  and 
a  back  view  of  it  is  represented  in  Fig.  29.  It  consists  in 
the  addition  of  a  clip,  behind  the  disk  holding  the  lenses,  into 
which  a  cylindrical  lens  can  be  placed.  This  clip  moves  in- 
dependently of  the  large  disk,  and  has  attached  to  it  a  section 
of  another  disk  holding  two  lenses,  +  3.5  and  —  3.5,  which 


IOO     OPHTHALMOSCOPES    WITH    CYLINDRICAL    ATTACHMENTS. 

can  be  brought  behind  the  .sight-hole  in  the  mirror  when 
needed.  The  degree  of  inclination  of  the  axis  of  the  cylinder 
is  read  off  on  a  scale  marked  at  the  edge  of  the  back  of  the 
mirror. 


REFRACTION  OPHTHALMOSCOPE  WITH  A  CLIP  FOR  THE  INSERTION  OF  CYLINDRICAL 

LENSES. 

Though  the  instrument  may  not  be  of  great  value  for  the 
first  determination  of  astigmatism,  it  is  very  useful  for  verifying 
the  findings  by  other  methods,  and  I  believe  will  be  found  very 
convenient  for  that  purpose,  after  some  practice  in  its  use. 

The  instrument  has,  too,  other  advantages  which  I  think  will 
commend  themselves  for  its  general  use.  By  the  use  of  the  two 
lenses  in  the  superposed  segment  a  large  number  of  lenses  are 
obtained  for  the  determination  of  general  ametropia.  We  can 
get.  in  all,  fifteen  plus  and  seventeen  minus  lenses,  as  follows  :  -f- 
0.5;  i;  1.5;  2;  2.5;  3;  3.554;  4.5;  5;  5.5;  6;  6.5;  7.5;  u; 
and  — 0.5;  i;  1.5;  2;  2.5;  3;  3.5;  4;  4.5;  5;  5.5;  6;  6.5; 


THE    INVERTED    OPHTHALMOSCOPIC    IMAGE. 


101 


7.5  59.5;  ii  ;  13.  These  are  all  that  are  ever  needed  in  prac- 
tice, and  the  interval  between  the  numbers  is  sufficiently  small 
for  the  finest  diagnosis.  Compared  with  other  instruments  of 
good  workmanship  and  equal  usefulness  the  price  is  very 
moderate  1. 

§  no.  Examination  by  means  of  the  inverted ophthalmoscopic 
image.  As  already  stated,  the  indirect  method  of  ophthalmo- 
scopic  examination  differs  essentially  from  the  direct  method. 
By  the  latter  we  look  immediately  upon  the  illuminated  fundus 
itself,  whereas  with  the  former,  we  see  its  actual  inverted  im- 
age formed  in  the  air  by  an  auxiliary  lens  placed  in  the  path 
of  the  emerging  rays. 


Fig.  jo. 


a 


FORMATION    OF  THE  ACTUAL  INVERTED  IMAGE  IN  THE  INDIRECT  METHOD  OF. 
OPHTHALMOSCOPIC  EXAMINATION. 

• 

The  size  and  position  of  this  aerial,  image  varies  with 
the  optical  condition  of  the  eye  from  which  the  rays  proceed, 
the  strength  of  the  auxiliary  lens  used,  and  under  certain  cir- 
cumstances on  the  distance  of  this  lens  from  the  cornea.  The 
problems  in  connection  with  this  method  of  observation  are 
therefore,  somewhat  more  complicated  than  in  the  direct 
method.  They  are  easily  solved,  however,  when  we  bring  to 
our  aid  a  few  of  the  fundamental  principles  of  optics. 

Let  us  examine  briefly  into  the  manner  in  which  this  inverted 
aerial  image  is  formed.  In  Fig.  30  E  is  an  emmetropic  eye 

1  The  instrument  is  made  by  A.  Meyer's  Sons,  93  William  street,  New  York.  Its 
price  is  $17.00.  The  clip  behind  the  mirror  can  be  made  by  them  to  fit  the  cylin- 
ders of  any  particular  trial-case. 


IO2  THE  SIZE  OF  THE  INVERTED  IMAGE. 

whose  fundus  is  already  illuminated.  From  the  points  o 
and  b  there  proceed  rays  which,  in  passing  out  of  the  eye,  be- 
come parallel.  These  rays,  falling  on  the  convex  lens  L.,  hav- 
ing a  focal  distance  of  3  inches,  are  brought  together  and  form 
at  the  focus  of  the  lens  an  inverted  image,  a  c,  of  o  b.  The  eye 
of  an  observer  at  0  will  see  this  image  a  c  clearly  when  it  is 
accommodated  for  vision  ai  that  distance.  The  power  of  the 
lens  L  governs  the  size  of  the  image  a  c  and  its  position  in  re- 
spect to  L. 

§  ill.  When  the  eye  is  emmetropic,  a  c  is  always  found  at 
the  focus  of  L,  no  matter  at  what  distance  from  the  observer's 
eyes  the  auxiliary  lens  is  held,  because  the  rays  come  from  the 
eye  parallel  and  remain  so  indefinitely,  and  will  consequently 
always  fall  thus  on  the  lens  at  whatever  distance  from  the  eye 
they  may  strike  it.  If  a  -t-1/*  ls  used,  the  image  will  always  be 
3  inches  in  front  of  it:  if  a  -\-l/->  is  employed,  it  will  be  2 
inches,  and  so  on. 

This  being  the  case,  with  the  same  lens  the  size  of  the  im- 
age a  c  must  always  be  the  same  in  emmetropia,  at  whatever 
distance  from  E  the  lens  is  held. 

This  is  true  of  the  actual  size  of  the  image,  but  not  strictly 
so  as  to  its  apparent  size  to  the  observer  at  O.  The  effect  of 
removing  L  away  from  E  would  be  to  cause  an  approximation 
of  the  image  a  c  to  O.  As  a  consequence  of  this  it  will  be 
seen  under  a  constantly  increasing  visual  angle  and  as  it  is  seen 
with  only  one  eye  and  is  always  referred  to  the  same  position 
in  space,  its  apparent  size  increases  as  it  is  brought  closer  to  O. 
It  is  not  strictly  true,  then,  as  stated  by  many  authorities  in 
ophthalmoscopy,  that  in  emmetropia  the  size  of  the  inverted 
image  remains  unchanged  in  all  positions  of  the  auxiliary  lens. 

§  112.  In  myopic  and  hypermetropic  eyes  we  have  an  entire- 
ly different  set  of  conditions  to  deal  with.  The  rays  coming 
from  the  illuminated  fundus  of  these  eyes  do  not  emerge  in 
a  state  of  parallelism,  but  are  either  convergent  or  divergent. 

The  size  and  position  of  the  image  produced  by  the  auxil- 
iary lens,  under  these  circumstances,  must  be  determined  by 
the  laws  of  conjugate  foci. 


VARIATION    OF    SIZE    OF    IMAGE    IN    H. 


103 


By  applying  these  laws  to  the  two  abnormal  optical  condi- 
tions of  myopia  and  hypermetropia  we  can  know  the  position, 
and  relative  size  of  the  image  to  its  object  in  any  given  position 
of  the  auxiliary  lens  on  the  common  optical  axis. 

§  1 13.  Let  us  take  the  case  of 'hypermetropia  first.  Here  the  rays 
emerge  divergent,  and  those  coming  from  the  point  o,  Fig.  31, 


CHANGE   IN  THE  SIZE  AND  POSITION  OF  THE  REAL  IMAGE  OF  THE  HYPERME- 
TROPIC  EYE  IN  THE  INDIRECT  METHOD  OF  OPHTHALMOSCOPIC  EXAMINATION. 

after  passing  out  of  the  eye  assume  a  direction  as  though  they 
cd.me  from  a  point  a  behind  the  eye,  which  is  the  virtual  and 
.eTect  image  of  o  formed  by  its  refracting  media.  This  point  a 
is  the  far  point  of  the  eye,  and  in  this  case  negative.  The  point 
a,  therefore,  and  not  o,  becomes  one  of  the  two  conjugate  foci 
and  gives  the  position  of  the  object,  whose  real  inverted  aer- 
ial image  is  to  be  formed  by  the  auxiliary  lens  placed  in  front 
of  the  eye.  When  this  lens  is  at  3,  (3  inches  in  front  of  the 
cornea)  the  image  of  the  object  at  a  will  be  formed  at  f,  a  dis- 
tance greater  than  the  focus  of  the  lens,  When  it  is  removed 
two  inches  farther  to  5,  the  image  will  be  formed  at  ^,  since 
in  bi-convex  lenses  the  object  and  the  image  are  displaced  in 
the  same  direction,  and  being  closer  to  the  lens  will  be  smaller. 
As  the  lens  is  still  further  removed  from  a  the  image  will  be 
brought  closer  to  the  lens  and  diminish  correspondingly  in  size 
until  it  reaches  a  point  where  the  emergent  rays  become  prac- 
tically parallel,  when  the  image  will  be  formed  at  the  focus  of 
the  lens,  and  will  then  remain  of  the  same  size,  even  though 
the  lens  were  removed  to  infinity. 

§  114.     In  myopia  the  conditions  are  the  reverse  of  those  in 


IO4 


VARIATION    OF    SIZE    OF    IMAGE    IN    M. 


hypermetropia,  and  there  is  a  corresponding  change  in  the  ef- 
fect on  the  position  and  size  of  the  image  formed  by  the  aux- 
iliary lens.  Here  again  we  can  assume,  for  the  sake  of  uni- 
formity, that  the  object  is  not  at  the  point  o  (Fig.  32)  from 
which  the  rays  emanate,  but  at  the  far  point  a,  where  the  emerg- 


32. 


A 


s       n 


SHOWING  HOW  THE  REAL  IMAGE  OF  THE  MYOPIC  EYE  VARIES  IN  SIZE  ON 
REMOVAL  OF  THE  AUXILIARY  LENS  IN  THE  INDIRECT  METHOD  OF  OPHTHAL- 
MOSCOPIC  EXAMINATION. 

ing  rays  meet  and  form  a  real  and  inverted  image  of  the  ob- 
ject at  o.  The  image,  formed  by  the  auxilliary  lens  placed  in 
the  path  of  these  rays,  will  be  real  and  on  the  same  side  of  the 
lens  as  the  object,  when  the  lens  is  found  at  any  place  between 
a  and  the  eye  M.  When  the  lens  is  at  I  (i  inch  in  front  of  M) 
the  image  which  is  seen  by  the  observer  will  be  at/,  nearer  the 
lens  and  smaller  than  the  object  at  a.  When  the  lens  is  ad- 
vanced towards  the  object  and  is  found  at  2,  according  to  the 
law  of  conjugate  foci,  the  image  advances  toward  the  lens,  is 
found  at  e,  and  is  increased  in  size.  As  the  lens  is  still  further 
removed  towards  a,  the  image  gets  nearer  and  nearer  the  lens 
and  increases  more  and  more  in  size,  but  still  remaining  real, 
until  it  is  found  at  7,  and  occupies  the  same  position  as  the  ob- 
ject. The  image  and  object  will  then  be  of  the  same  size,  one 
lying  at  the  first  nodal  point  of  the  lens,  /•,  the  other  at  the 
second  nodal  point,  k' .  On  a  still  further  removal  of  the  lens 
a  is  left  between  it  and  the  eye,  the  image  becomes  virtual,  is 
found  between  the  lens  and  the  eye  M,  and  is  larger  than  the 
object  at  a.  It  continues  to  increase  in  size  on  further  removal 


VARIATION    OF    SIZE    OF    IMAGE    IN    M.  10$ 

of  the  lens  until  the  lens  is  found  at  9,  when  the  object  lies  at 
its  focal  distance.  The  rays  will  then  emerge  from  the  lens 
parallel,  /  n,  m  i,  and  the  image  will  lie  at  infinity  and  be  in- 
finitely large  as  compared  with  the  object. 

When  the  lens  gets  beyond  its  focal  distance  from  the  object 
at  a,  as  at  1 1,  the  rays  s  t,  r p  emerge  from  it  convergent,  and 
will  form,  somewhere  beyond,  an  inverted  and  real  image  of  the 
object  at  a,  being  a  real  and  erect  image  of  o.  As  the  lens  is 
still  further  removed  this  real  image  approaches  the  lens  and 
becomes  smaller. 

§  115.  This  variation  in  the  size  of  the  real  image  of  the 
myopic  eye  on  removal  of  the  auxiliary  lens,  can  be  demon- 
strated by  taking,  as  one  of  the  conjugate  foci,  the  actual  object 
at  o ;  but  in  that  case  we  should  have  to  do  it  with  a  constantly 
varying  compound  optical  system  of  the  eye  and  the  lens, mak- 
ing the  problem  much  more  complicated.  We  have  taken  the 
images  (virtual  and  real),  formed  at  the  far  points  in  the  two 
states  of  ametropia,  for  the  sake  of  uniformity  and  for  ease  of 
demonstration  and  comparison  in  the  two  conditions. 

§  116.  It  is  apparent  from  the  foregoing,  that  it  cannot  be 
strictly  true,  as  has  been  commonly  stated  in  a  general  way 
without  qualification,  that  the  inverted  image  of  the  myopic  eye 
is  smaller  than  that  of  the  hypermetropic  eye  when  both  are 
formed  by  the  same  lens.  The  relative  size  of  the  inverted 
image,  as  we  have  seen,  depends  entirely  on  the  place  occupied 
by  the  auxiliary  lens  on  the  optical  axis,  and  there  are  some 
positions  of  the  lens  in  myopia — when  it  is  near  the  far  point  of 
the  eye  under  examination — where  it  will  be,  not  only  rela- 
tively, but  actually  larger  than  the  image  of  a  hypermetropic 
eye  of  the  same  degree  produced  by  the  same  lens  in  the  same 
position  as  regards  the  eye. 

§  117.  These  general  rules  in  regard  to  the  size  of  the  in- 
verted image  of  the  myopic  and  hypermetropic  eye  are  equally 
applicable  to  the  myopic  and  hypermetropic  meridians  of  the  as- 
tigmatic eye.  The  effect  upon  the  image  caused  by  the  dis- 
placement of  the  auxiliary  lens  is  of  a  peculiar  character  and 
different  in  the  different  forms  of  the  anomaly.  An  observa- 


IO6  VARYING  SHAPE  OF  THE  DISK  IN  ASTIGMATISM. 

tion  of  these  changes  is  most  useful  in  making  the  diagnosis  of 
the  «form  of  astigmatism  from  which  the  eye  may  suffer,  and 
gives  us  a  general  idea  of  the  direction  of  the  principal  me- 
ridians and,  in  a  rough  way,  of  the  amount  of  the  astigmatism. 

§  1 1 8.  In  the  simple  form  of  myopic  astigmatism,  when  the 
lens  is  gradually  removed  from  its  ordinary  position  at  from  I 
to  2  inches  in  front  of  the  cornea  towards  the  far  point  of  the 
eye,  there  will  be  a  progressive  enlargement  of  the  optic  disk 
in  the  myopic  meridian,  while  the  diameter  of  the  disk  which 
corresponds  to  the  emmetropic  meridian  will  remain  un- 
changed. If,  for  instance,  the  vertical  is  the  myopic  meridian, 
the  surface  of  the  disk  instead  of  being  round  will  appear 
drawn  out  vertically,  and  the  amount  and  the  rapidity  of  the 
elongation  will  be  in  proportion  to  the  degree  of  the  myopia  in 
that  meridian.  Should  the  myopic  meridian  be  oblique,  the 
inclination  of  the  oval  disk  will  correspond  to  the  direction  of 
the  faulty  meridian.  It  must  be  borne  in  mind,  in  this  connec- 
tion, that  owing  to  the  inward  rotation  of  the  eye  necessary  to 
bring  the  optic  disk  into  view  in  ophthalmoscopic  examina- 
tions, the  disk  is  seen  somewhat  in  profile  and  in  the  normal 
eye  does  not  generally  appear  round,  but  vertically  oval.  For 
the  diagnosis  of  a  myopia  in  the  vertical  meridian,  therefore, 
the  oval  in  this  direction  must  increase  as  the  lens  is  removed 
from  the  eye. 

When,  on  the  other  hand,  the  lens  is  brought  very  close  to 
the  cornea,  the  horizontal  (emmetropic)  diameter  remains  un- 
altered, while  the  vertical  (myopic)  diameter  gradually  dimin- 
ishes in  size,  assuming  finally,  if  sufficiently  close,  a  horizontal 
oval  form. 

§  119.  In  compound  myopic  astigmatism,  we  have,  in  accord- 
ance with  the  facts  just  stated,  a  general  progressive  enlarge- 
ment of  the  disk  on  removal  of  the  lens,with  a  greater  enlarge- 
ment and  drawing  out  of  that  diameter  of  the  disk  correspond- 
ing to  the  meridian  most  strongly  myopic,  while  there  is  a 
greater  shortening  of  the  same  diameter  when  the  lens  is 
brought  very  close  to  the  cornea. 

§  1 20.     We   have,    of  course,    an    entirely    different   set  of 


VPPEARANCE  OF  THE  FUNDUS  BY  THE  INDIRECT  METHOD.       IO/ 

cnanges  in  hypermetropic  astigmatism.  Example:  As  the  lens  is 
withdrawn  from  the  eye,  the  vertical  diameter  remains  essen- 
tially unchanged, while  the  horizontal  diameter,  corresponding  to 
the  hypermetropic  meridian,  becomes  more  and  more  contrac- 
ted. Diagnosis  :  Simple  hypermetropic  astigmatism,  axis  vertical. 
§  121.  In  compound  hypermetropic  astigmatism  there  is,  on 
withdrawal  of  the  lens,  a  narrowing  of  the  disk  in  all  its  diame- 


APPEARANCE  OF  THE  FUNDUS  OF  AN  EYE  WITH  MIXED  ASTIGMATISM,  WHEN  THE 
AUXILIARY  LENS  is  HELD  CLOSE  TO  THE  CORNEA. 

ters,  but  it  is  more  rapid  in  the  diameter  corresponding  to  the 
most  hypermetropic  meridian.  The  result  is  an  oval  with  its 
short  diameter  in  the  direction  of  the  meridian  of  least  refrac- 
tion, the  same  as  in  the  myopic  forms,  but  it  is  produced  in  a 
diametrically  opposite  manner.  In  the  hypermetropic  forms  it 
is  the  result  of  contraction  in  the  faulty  meridian ;  in  the  myopic 
forms  it  is  due  to  enlargement  in  the  direction  of  the  faulty  me- 
ridian. 

§  122.  The  most  marked  picture,  however,  is  that  furnished 
by  the  mixed  form  of  astigmatism.  Let  there  be,  for  example, 
(as  in  the  case  from  which  the  accompanying  drawings  were 
taken),  hypermetropia  of  3  D  in  the  vertical  meridian,  and  my- 
opia of  7  D  in  the  horizontal  meridian.  We  have  here  the  con- 


IO8       APPEARANCE  OF  THE  FUNDUS  BY  THE  INDIRECT  METHOD. 

ditions  necessary  for  producing  the  combined  effects  of  both 
these  optical  states  in  a  very  pronounced  manner.  When  the 
lens  is  held  very  close  to  the  cornea  the  enlargement  in  the  hy- 
permetropic  (horizontal)  meridians  is  at  its  greatest,  while  the 


APPEARANCE  OF  THE  FUNDUS  OF  AN  EYE  WITH  MIXED  ASTIGMATISM,  \YHKN  THE 
AUXILLIARY  LENS  IS  AT  A  GREAT  DISTANCE  FROM  THE  CORNF.A. 

contraction  in  the  myopic  (vertical)  meridian  is  at  its  minimum. 
As  a  consequence  the  disk  is  elongated  horizontally,  while  the 
retinal  vessels  are  drawn  together  and  take  a  more  horizontal 
direction  (Fig.  33).  As  the  lens  is  gradually  removed  from 
this  position  the  horizontal  (hypermetropic)  diameter  progres- 
sively contracts,  the  vertical  (myopic)  diameter  progressively 
enlarges,  and  the  vessels  turn,  as  it  were,  on  a  pivot,  becoming 


KNAPP'S,  SCHWEIGER'S  AND  BRAVAIS'  METHODS.         109 

more  and  more  vertical  until  a  point  is  reached  where  we  have 
the  appearances  given  in  Fig.  34  in  which  the  enlargement  in 
the  vertical  (myopic)  meridian  is  greatest,  and  the  diminution 
in  the  hypermetropic  (horizontal)  meridian  approaches  its 
minimum. 

§  123.  These  examinations  should  be  made  with  a  lens  of 
short  focus — two  inches  at  most — since  a  strong  lens  gives 
a  large  ophthalmoscopic  field,  which  with  a  wide  pupil,  is  al- 
most indispensable  for  a  satisfactory  diagnosis. 

§  124.  The  chief  defect  of  the  method  is  the  lack  of  accuracy 
in  determining  the  degree  of  astigmatism.  This,  as  well  as  the 
direction  of  the  principal  meridians,  can  be  only  roughly  esti- 
mated by  the  rapidity  of  change  in  the  form  of  the  disk  on 
moving  the  lens,  and  the  direction  of  the  long  axis  of  the  oval. 
Its  value  lies  in  the  knowledge  it  gives  us  of  the  existence  and 
form  of  astigmatism  in  those  cases  where  the  amblyopia  or 
stupidity  of  the  patient  makes  it  difficult  or  impossible  to  ob- 
tain reliable  data  by  any  one  of  the  subjective  methods  of  ex- 
amination. 

§  125.  Knapp  and  Schweiger  have  called  attention  to  the 
change  in  the  form  of  the  disk,  when  seen  successively  by  the 
direct  and  indirect  methods  of  examination,  as  a  means  of  di- 
agnosing astigmatism.  The  erect  image  of  the  disk  in  both 
M  and  H  is  oval,  with  its  short  diameter  in  the  direction  of 
the  meridian  of  least  refraction ;  in  the  inverted  image,  on  the 
other  hand,  the  short  diameter  coincides  with  the  meridian  of 
greatest  refraction.  This,  however,  is  true  only  when  the 
auxiliary  lens  is  held  at  the  ordinary  position  near  the  eye. 
When  it  is  removed  to  any  considerable  distance  from  it,  as 
we  have  seen,  there  is  a  change  to  the  opposite  condition,  and 
the  oval  is  the  same  as  in  the  direct  method. 

§  126.  Bravais,  of  Lyon,  suggested  a  method  based  on  the 
associated  movements  of  the  lens  and  image.  When  the  disk 
is  in  the  center  of  the  lens  and  the  latter  is  moved  from  side  to 
side,  if  there  is  emmetropia  the  lens  and  image  move  together. 
In  myopia  the  movement  of  the  image  is  less  than  that  of  the 
lens ;  in  hypermetropia  it  is  greater.  By  moving  the  lens  in 


1IC  COUPERS     METHOD. 

various  directions  perpendicular  to  the  optical  axis,  and  noting 
the  amount  of  displacement  of  the  image,  some  idea  may  be 
formed  of  the  direction  of  the  principal  meridians  and  the  kind 
of  refraction  in  each. 

§  127.  In  this  and  in  all  the  methods  of  examination  with 
an  auxiliary  lens,  great  care  should  be  taken  to  hold  the  lens 
strictly  at  right  angles  to  the  visual  axis,  for  otherwise  we 
would  have  the  cylindrical  action  resulting  from  an  oblique 
position  of  the  spherical,  which  might  be  misleading  as  to  the 
optical  condition  of  the  eye. 

§  128.  Mr.  Couper  has  suggested  a  method  of  examination 
by  the  mirror  alone  for  the  observation  of  the  inverted  and 
erect  images,  successively,  which  is  available  particularly  for 
the  detection  of  the  mixed  and  simple  forms  of  astigmatism. 
For  this  purpose  he  employs  a  mirror  of  30  inches  focus 
and  places  himself  at  a  distance  of  4'/2  to  5  feet  from  the  pa- 
tient. He  is  then  in  a  position  to  see  an  inverted  aerial  imaged 
of  the  fundus  formed  by  the  meridian  having  a  myopia  of  iD 
or  more.  This  image  may  be  only  a  portion  ol  a  vessel  or  a 
part  of  the  edge  of  the  optic  disk,  and  will  be  larger  and 
formed  farther  from  the  eye  the  lower  the  degree  of  the  my- 
opia, while  the  direction  in  which  the  vessel  or  vessels  appear 
to  run  will  be  at  a  right  angles  to  the  faulty  meridian.  If  the 
other  meridian  is  emmetropic  or  hypermetropic,  of  course  no 
vessels  or  other  details  of  the  fundus  lying  in  that  direction 
can  have  their  images  formed  at  that  distance,  and,  therefore, 
cannot  be  seen.  These  come  into  view  only  when  the  mirror 
is  brought  closer  to  the  eye,  when  they  will  be  seen  directly 
and  erect,  while  the  vessels  in  the  other  meridian  will  have 
vanished. 

§  129.  Schmidt-Rimpler  claims  that  his  plan  for  estimating 
refraction  by  the  inverted  image  is  applicable  for  the  diag- 
nosis of  astigmatism.  In  this  method  of  examination  the  ob- 
server does  not  look  at  the  retinal  vessels  or  other  details  of 
the  fundus,  but  at  the  aerial  image  of  a  gas-flame  or  illumi- 
nated fret-work  which  serves  as  the  source  of  illumination. 

The  manner  in  which  this  image  is  produced  is  as  follows : 


SCHMIDT-RIMPLER  S    APPARATUS.  Ill 

A  fret-work  of  small  squares  and  triangles,  made  in  a  screen, 
is  placed  before  the  flame  of  gas  or  a  lamp.  With  a  concave 
mirror  of  short  focus  (20  cm.)  an  image  of  this  brilliant  fret- 
work is  formed  in  front  of  the  observed  eye,  and  becomes  the 
source  of  its  illumination.  An  auxiliary  lens  of  a  certain  focus 
(10  cm.)  is  held  at  a  fixed  distance  (10  cm.)  from  the  eye  to  be 
examined,  and  the  combined  power  of  the  lens  and  the  re- 
fracting apparatus  of  the  eye  form  an  image  of  this  open  work 
in  its  fundus.  This  retinal  image  of  the  fret-work  will  be 
sharply  defined  only  when  the  trellis-work  image  in  the  air 
and  the  fundus  are  at  conjugate  foci,  and  when  this  relation 
exists  there  will  be  formed,  according  to  the  law  of  conjugate 
foci,  at  the  source  of  illumination  a  sharply  defined  image  of 
the  retinal  image,  and  this  it  is  which  the  observer  sees. 

Now,  the  distance  from  the  lens  at  which  this  distinct  aerial 
image  will  be  formed  depends,  as  we  have  seen  in  §  107  (the 
auxiliary  lens  and  its  distance  from  the  eye  being  constant 
quantities),  upon  the  refracting  power  of  the  eye.  It  is  farther 
from  the  lens  in  H  and  closer  to  it  in  M  than  it  is  in  E.  If  we 
have  a  means  of  measuring  this  distance,  the  determination  of 
the  kind  and  even  the  degree  of  ametropia  becomes  easy. 
This  has  been  made  possible  by  Schmidt-Rimpler,  through  a 
very  simple  arrangement.  The  power  of  the  auxiliary  lens 
and  its  distance  from  the  eye  being  always  the  same,  and  the 
image  of  the  fret-work  being  always  at  20  cm.  from  the  mirror, 
it  is  only  necessary  to  approach  the  mirror  to  the  eye  until  the 
aerial  image  becomes  sharply  defined,  measure  the  distance 
between  the  mirror  and  lens,  and  subtract  20  from  the  dis- 
tance, in  order  to  have  the  distance  of  the  image  from  the 
lens.  If  a  lens  of  10  cm.  focal  distance  is  used,  the  image  will 
be  formed  in  emmetropia  at  10  cm.  in  front  of  it,  since  the 
rays  emerging  from  the  eye  strike  it  parallel ;  in  myopia,  the 
distance  of  the  image  from  the  lens  will  be  shorter,  in  hyper- 
metropia,  greater.  For  a  lens  of  10  D  (10  cm.  focus)  it  has 
been  found  that  every  variation  of  I  cm.  from  this  distance  of 
10  cm.  corresponds  to  a  difference  in  refraction  amounting  to 
iD.  This  measurement  he  makes  by  means  of  a  roller  tape, 


112  SCHMIDT-RIMPLER  S   APPARATUS. 

the  roller  end  of  which  is  attached  below  the  lens,  while  the 
free  end  is  held  at  the  mirror. 

The  manner  of  making  the  observation  is  as  follows :  the 
auxiliary  lens  is  fixed  near  the  end  of  a  small  bar  graduated 
in  centimetres,  and  under  it  is  the  roller  tape,  which  winds  up 
with  a  spring.  The  free  end  of  this  bar  is  placed  on  the  lower 
edge  of  the  orbit,  and  when  the  lens  is  at  9.5  cm.  it  is  about 
10  cm.  in  front  of  the  principal  points  of  the  eye.  The  mirror, 
to  which  the  free  end  of  the  measuring  tape  is  attached,  is 
placed  at  40  to  50  cm.  from  the  auxiliary  lens  and  the  fundus 
of  the  eye  illuminated  in  the  usual  manner.  The  aerial  image 
of  the  fret-work  will  then  be  seen  as  an  ill-defined  bright  spot. 
As  the  mirror  is  approached  closer  to  the  lens  it  becomes  more 
and  more  clear  in  outline,  and  finally  one  position  is  found  in 
which  all  the  details  are  sharply  defined:  The  distance  of  the 
mirror  from  the  lens  is  then  read  off  on  the  measuring  tape 
and  20  taken  from  it.  The  remainder  is  the  distance  of  the 
image  from  the  lens.  The  difference  between  this  number 
and  10  gives  the  amount  of  ametropia.  If,  for  example,  the 
distance  between  lens  and  mirror  is  35  cm.  the  distance  of  the 
image  from  the  lens  is  (35 — 20)  15  cm.  and  there  is  H  of  15 
—  10  =  5  D,  each  cm.  corresponding  to  I  D  of  refracting 
power.  If  it  is  27  cm.  the  ametropia  is  M  (27  —  20  =  7  ;  IO 
-  7)  =  3  D. 

In  astigmatism,  from  what  has  already  been  abundantly 
demonstrated,  it  is  apparent  that  in  no  single  position  of  the 
mirror  can  the  lines  of  the  figures  of  the  fret-work  at  right  an- 
gles to  each  other  be  seen  with  equal  clearness,  since  the  im- 
age of  one  set  of  lines  will  be  formed  sharply  at  one  place 
and  that  of  the  other  at  another.  Taking  advantage  of  this 
fact,  we  approach  the  mirror  until  the  lines  of  the  figure  run- 
ning in  some  one  direction  are  seen  with  the  greatest  distinct- 
ness and,  read  off  on  the  tape-measure  the  distance  of  the  mir- 
ror. This  gives  us  the  refracting  power  of  the  meridian  of  least 
refraction.  The  mirror  is  then  brought  closer  to  the  eye  until 
the  lines  at  right  angles  to  these  are  seen  sharply ;  the  dis- 
tance of  the  mirror  read  off  on  the  tape  then  gives  the  re- 


VALUE    OF    THE    DIFFERENT    METHODS.  113 

fraction  in  the  most  highly  refracting  meridian,  and  the  differ- 
ence between  the  two  shows  the  amount  of  the  astigmatism. 
Example  :  The  lines  running  vertically  are  seen  at  34  cm., 
those  running  horizontally  at  31  cm.;  there  is  compound  hy- 
permetropic  astigmatism.  In  the  vertical  meridian  there  is  H 
(31  —  20  =  II  ;  ii  —  10  —  i)  of  i  D;  in  the  horizontal  H 
(34  —  20  =  14 ;  14  —  10  =  4)  of  4  D ;  H  =  i  D  with  astig. 
=  3  D  axis  90°. 

§  130.  My  own  experience  convinces  me,  however,  and  I 
believe  the  opinion  will  be  corroborated  by  most  ophthal- 
moscopists,  that  the  two  methods  of  examination  by  the  erect 
and  inverted  images  as  usually  employed,  and  as  described  in 
§§  99  to  126,  if  cultivated  with  the  care  which  their  importance 
in  other  particulars  demands,  are  capable  of  furnishing  us  with 
all  the  information  in  regard  to  the  refraction  of  the  eye  that 
the  ophthalmoscope  is  capable  of  giving. 

The  data  thus  obtained  are  often  very  accurate,  but  the  lia- 
bility to  error  is  too  great  for  any  one  of  these  methods  to  be 
relied  upon  implicitly.  Before  ordering  glasses,  the  findings 
with  the  ophthalmoscope  should  be  verified  by  an  examina- 
tion with  cylindrical  lenses  and  the  test  letters. 

BIBLIOGRAPHY. 


Bravais — Du  diag.  ophthalmoscopique  de  1'astig.     Lyon  Med.     VII.     Pp.  319-25. 

1875- 

Carreras,  Arago — El  oltalmsc.  de  refrac  en  los  reconocimientos  visuales.  Rev.  d. 
cien.  Med.  VIII.  P.  3.  Barcel.  1882. 

Cohn,  H. — Ein  Augenspiegl.  f.  schnell.  Refractbestim.  Klin.  Monatsbl,  f.  Au- 
genhlk.  X.  Pp.  307-9.  1872. 

Couper,  J. — On  a  new  and  simple  meatis  of  detect,  mxd.  astig.  by  the  ophth.  Med. 
Times  and  Gaz.  London.  I.  P.  114.  1866. 

Couper,  J. — The  ophth.  as  an  optometer  in  astig.  Rep.  Internat.  Ophth.  Cong. 
London.  1872.  Pp.  109-19.  1873. 

Dennett,  W.  S. — Astig.;  the  fundus  of  astig.  eyes ;  an  attachmt.  to  the  ophth. 
Arch.  Ophth.  and  Otol:  N.  Y.  V.  Pp.  505-7.  1876. 

Dennett,  W.  S. — Zur  Untersuch.  astig.  Augen  mit  dem  Augenspiegel.  Arch. 
Ohr.  u.  Augenhlk.  VI— I.  P.  55.  1877. 

Frothingham,  G.  E. — A  case  of  mxd.  astig.  with  predom.  myopia  diag.  by  itspecul. 
ophth.  appearance.  Phys.  and  Surg.  Ann  Arbor,  Mich.  II.  Pp.  14-16.  1880. 

Giraud-Teulon — La  vision  et  ses  anomalies.    Paris.     1881. 


1 14  BIBLIOGRAPHY. 

Giraud-Teulon — Theorie  de  1'ophthalmoscope  avec  les  deductions  qui  en  decou- 
lert  Gaz.  Med.  d.  Paris.  Nos.  7  et  8.  1859. 

Giraud-Teulon — De  1'influence  des  lentilles  positives  et  negatives  et  de  celle  de  leur 
distance  a  1'ooil  sur  les  dimensions  des  images  ophthalmoscopiques  de  la  papille 
ou  disque  optique  dans  les  anomalies  de  la  refraction  oculaire,  et  particulierement 
dans  1'astigmatisme.  Mem.  presente  a  1'Acad.  d.  Sci.  Aout  9.  1869. 

Hay,  G. — Apparent  form  of  inverted  ophth.  image  of  opt.  disc  in  Astig.  Trs. 
Amer.  Ophth.  Soc.  P.  86.  1870. 

Knapp,  H. — Demonstratof  the  refract  ot  light  by  asymmetric,  surfaces  and  the  de- 
terminat.  of  astig.  with  glasses  and  the  ophth.  Trs.  Am.  Med.  Ass.  XXXI.  Pp. 
669-74.  1880. 

Landolt,  E. — Le  grossement  des  images  ophthalmoscopiques.  Paris.  A.  De- 
laharye.  1874. 

L'Hoest — Du  diag.  des  anomal  de  refract,  de  1'oeil  au  moyen  de  1'ophth.  Arch. 
Med  Beiges.  XXI.  P.  177.  1882. 

Loring,  E.  G.— Text-book  of  ophthalmoscopy.  Part  I.  N.  Y.  D.  Appleton  & 
Co.  1886. 

Mauthner,  L. — Lehrbuch  der  ophthalmoscopie.    Wien.     1867. 

Parent — Descript.  d'un  ophth.  a  verres  cyld.  (nouveau  modelle).  Ann.  d'oculist. 
Sept.  Oct.  1883. 

Perrin,  M. — Traite  d'ophthalmoscopie   et   d'  optometrie.     Paris.     1870.     (Astig). 

Stammeshaus — Ueber  eine  methode  dem  aufrechten  Bilde  eine  starkere  Vergroes- 
serung  zur  erhielen.  Zehend.  Monatsbl.  f.  augenhsilk.  Jan.  1874. 

Schmidt-Rimpler — Zur  ophth.  Refractionsbestimmg.  mil  Hiilfe  des  umgekhrt. 
Bildes.  Tagebltt  d.  Naturfsohrsors.  zu  Kassel.  1878. 

Schmidt-Rimpler — Zur  cbjct  Refractsmsg.  Centralbl.  f  prakt.  Angenhlk.  P.  260. 
1878. 

Schmidt-Rimpler — Ophth.  Refrctsbestim.  im  umgekrt  Bilde.  Zeitschr.  f.  Instru- 
mentk.  Nov.  1882.  Also  in  Augenheilkunde  und  Ophthalmoscopie.  Braunschw. 
1885. 

Schweiger,  C. — Ueber  die  Groesse  des  ophthalmoscop.  Bildes.  Nachrichten  d. 
Koen.  Gesell.  d.  Wissensch.  u  d.  G.  A.  Univ.  et  Goettingen.  No.  9.  April,  1870. 

Schnabel — Ueber  die  Lage  und  Groesse  des  aufrechten  Bildes  in  Augenhinter- 
grunde.  Zehenders  Monatbl.  f.  Augenheilk.  1872.  P.  117. 

Snellen,  H.  and  Landolt,  E. — Ophthalmometrologie.  in  Handbuch.  d.  gesammt. 
Augenheilk.  von  Grafe  u.  Samisch.  B.  II.  I.  1874. 

Stilling — Ueber  ophthalmosc.  Refractsbestim.  Klin.  Monatsbl  f.  Augenheilkd.  B. 
XIII.  P.  143.  1875. 

Stimmel — Objct.  Bestming  d.  Astig.  Klin.  Monatsbl.  f.  Augenhlk.  XIII.  Pp. 
3902.  1875. 

Uhthoff — Demonstrat.  eines  Refracts  ophthalmo.  zur  Bestiming.  des  Astig.  Ber. 
U.  d.  versamml.  d.  ophth.  Geselsch.  Stuttg.  XIV.  P.  167.  1882. 


CHAPTER   VIII. 


SKIASCOPY.     (THE  SHADOW-TEST.) 

§  131.  In  a  foot  note  on  page  490  of  his  treatise  on  the 
'Anomalies  of  Accommodation  and  Refraction  of  the  Eye," 
Bonders  makes  the  following  record  : 

"  My  friend  Bowman  recently  informs  me  that  '  he  has  been 
sometimes  led  to  the  discovery  of  regular  astigmatism  of  the 
cornea,  and  the  direction  of  the  chief  meridians,  by  using  the 
mirror  of  the  ophthalmoscope  much  in  the  same  way  as  for 
slight  degrees  of  conical  cornea.  The  observation  is  more 
easy  if  the  optic  disk  is  in  the  line  of  sight  and  the  pupil  large. 
The  mirror  is  to  be  held  at  two  feet  distance  and  its  inclination 
rapidly  varied  so  as  to  throw  the  light  on  the  eye  at  small  an- 
gles to  the  perpendicular  and  from  opposite  sides  in  succession, 
in  successive  meridians.  The  area  of  the  pupil  then  exhibits  a 
somewhat  linear  shadow  in  some  meridians  rather  than  in  oth- 
ers.' " 

This  description  is  too  short  and  indefinite  to  enable  us  to  de- 
cide whether  these  experiments  of  Bowman  held  the  germ  of 
the  method  now  known  under  the  names  of  "  keratoscopy," 
"retinoscopy,"  "pupilloscopy,"  "phantoscopy,"  etc.,  but  at  all 
events  no  extensive  practical  application  was  made  of  the 
changes  observed  in  the  pupillary  area  when  illuminated  from 
a  distance  by  a  simple  mirror  until  the  publication  of  an  article 
on  the  subject  by  Cuignetinthe  Recueil  d'  Ophthalmologie  in 


§  132.  Most  of  the  names  given  to  the  method  do  not  con- 
vey any  intelligent  idea  of  the  nature  of  the  phenomena  on 
which  it  is  based.  The  appearances  do  not  pertain  either  to 
the  cornea,  pupil  or  retina  alone.  They  are  due  entirely  to  the 
refractive  condition  of  the  eye  as  a  whole.  As  the  principal 
and  distinguishing  feature  of  the  method  is  the  behavior  of  the 


OPTICAL    PRINCIPLES    OF    THE    SHADOW-TEST. 

shadowy  edges  of  the  bright  image  of  the  source  of  illumina- 
tion, "  the  shadow-test "  would  seem  to  be  the  most  appropriate 
term  by  which  it  could  be  designated.  If,  however,  we  should 
wish  to  use  a  general  scientific  term,  the  word  "  skiascopy,"  as 
suggested  by  the  celebrated  Greek  scholar,  M.  Egger,  is  avail- 
able. 

§133.  The  method  is  founded  on  the  observed  fact  that 
when  the  light  from  a  flame,  placed  in  the  ordinary  position  for 
ophthalmoscopic  examination,  is  thrown  into  the  eye  by  means 
of  a  mirror  at  a  distance  of  from  3  to  5  feet  from  the  eye, 
and  the  mirror  is  rotated  about  one  of  its  axes,  a  shadow  is  ob- 
served to  pass  across  the  bright  area  of  the  pupil.  The  relative 
brightness  of  the  pupil  and  the  direction  and  rapidity  with 
which  the  shadow  moves  serve  as  a  basis  for  diagnosis,  and  on 
the  following  principles : 

fig-  35- 


» 


SHOWING  THE  OPTICAL  PRINCIPLES  ON  WHICH  SKIASCOPY  is  BASED. 

§  134.  When  the  light  from  the  flame  F,  Fig.  35,  is  thrown 
by  a  concave  mirror  M  in  the  direction  of  the  eye  P,  from  a  dis- 
tance of  from  3  to  4  feet,  an  image  of  the  flame  is  formed,  near 
the  focus  of  mirror,  at  F1.  This  image  then  becomes  the  illum- 
inated object  from  which  rays  diverge  and  which,  passing  into 
the  eye  P,  form  an  image  on  its  retina  at  F*.  The  light  is  re- 
flected from  this  retinal  image  and  passing  out  of  the  eye  forms 
in  its  turn  an  image  real  or  virtual  at  a  certain  place  before  or 
behind  the  eye,  according  to  its  refractive  condition. 

§  135.     Let   us    suppose,    for    illustration,    that    F1    is  one 


OPTICAL    PRINCIPLES    OF    THE    SHADOW-TEST.  1 1/ 

meter  from  K  the  nodal  point  of  the  eye  P.  Then,  if  P  is  em- 
metropic,  the  image  of  F1  formed  on  the  retina  at  F2,  which  in 
this  case  will  be  blurred  in  outline,  will  send  out  rays  that  will 
be  rendered  parallel  by  the  refracting  media  and  an  image  of 
F-  will  be  formed  at  infinity,  behind  the  observer's  eye  at  O. 
When  the  mirror  is  rotated  to  the  position  of  M1,  the  source  of 
illumination  moves  from  F1  to/1  and  the  retinal  image  moves 
from  F*  to/2.  To  the  observer's  eye  at  O  the  movement  of 
the  image  of/2  formed  at  infinity  by  the  refracting  media  of  P 
is  in  the  sense  contrary  to  the  movement  of  the  mirror,  and  the 
extent  of  this  movement  is  infinitely  large  as  compared  to  that 
of  the  mirror. 

If,  however,  the  eye  is  myopic  with  its  far  point  at  F*,  the 
retinal  image  F2  will  form  a  real  and  inverted  image  of  itself  at 
that  point.  When  the  mirror  is  rotated  to  Ml  the  image  of  /2 
will  move  from  F*  to  /*  in  the  same  sense  with  the  mirror. 
The  amount  of  movement  will  be  measured  by  the  distance 
from  F*  to/4.  Should  the  far  point  of  the  myopic  eye  lie  at  F5 
the  image  of  F'2  will  be  found  there,  and  on  rotation  of  the  mir- 
ror, move  to/5, likewise  with  the  mirror.  The  amount  of  move- 
ment is  measured  by  the  distance,  F'°f'3. 

It  will  be  seen  from  this  that  the  movement  is  less  the  greater 
the  degree  of  myopia,  and  greater  the  smaller  the  degree.  * 

§  1 36.  When,  as  in  hypermetropia,  the  image  of  F2  is  virt 
and  behind  P,  the  character  of  its  movements  is  changed.  If  it 
is  found  at  **,  for  example,  on  rotation  of  the  mirror  to  Ml  F3 
will  move  in  an  opposite  direction  to/3  and  the  extent  of  move- 
ment will  be  expressed,  as  before,  by  the  distance  F3/3.  The 
farther  F3  is  removed  from  K,  that  is  the  lower  the  degree  of 
hypermetropia,  the  greater  the  amount  of  movement,  until  it 
reaches  its  maximum  when  the  rays  coming  from  it  become 
practically  parallel,  and  the  eye  essentially  emmetropic.  The 
closer  F2  approaches  to  K,  that  is  the  higher  the  degree  of  hy- 
permetropia, the  less  the  amount  of  movement. 

§  137.  From  the  foregoing  the  following  facts  are  estab- 
lished :  i.  That  in  emmetropia  and  hypermetropia  the  move- 
ment of  the  image  is  against  that  of  the  mirror.  2.  That 


Il8  DIAGNOSIS  OF  AMETROPIA  BY  THE    SHADOW-TEST. 

in  myopia  of  degrees  above  iD,  that  is  when  the  far  point  of 
the  eye  is  within  3  feet,  the  movements  are  with  the  mirror.  3. 
That  in  both  forms  of  ametropia  the  higher the  degree  the  less 
the  extent  of  movement. 

§  138.  But  this  is  not  all.  The  brightness  of  the  image  changes 
with  the  degree  of  ametropia.  If  F*  coincides  with  the  far 
point  of  the  observed  eye  (there  being  M  of  iD),  the  image  F2 
will  be  clear  and  distinct,  and  all  rays  proceeding  from  it  will 
come  back  and  be  again  united  at  F1.  There  will  then  be  a 
maximum  of  brightness  of  the  image  seen  by  the  observer  O. 
If,  however,  F2  should  not  be  the  conjugate  focus  of  F1  there 
will  be  circles  of  diffusion  at  F2  which  will  be  large  in  propor- 
tion to  the  departure  in  either  way  from  this  M  of  iD.  Each 
individual  point  of  F2  will,  therefore,  have  fewer  rays  coming 
from  it,  and  there  will  be  a  diffusion  of  them  over  a  greater  ex- 
C-  tent  of  surface,  with  a  corresponding  diminution  in  distinctness 
of  the  image. 

§139.  Now,  what  we  specially  note  in  this  method  of  exam- 
ination is  the  shadowy  outline  of  this  circle  of  diffusion  which  is 
so  large  in  ametropia  that  the  edges  appear  as  almost  straight 
lines,  and  its  diagnostic  value  is  summarized  as  follows  : 

1.  Movement  of  shadow  edge  against  the  mirror,  low  degree 
of  M,  (less  than  i.D)  emmetropia,  or  hypermetropia  ;  extent  of 
movement  less  the  higher  the  degree  of  hypermetropia.  Bright 
reflex ;  E.  or  low  degrees  of  M.  or   H  :  dull  reflex,   higher  de- 
grees of  H. 

2.  Movement  of  shadow  with  the  mirror ;  M.  above  i  D,  its 
extent  diminishing  as  the  degree  increases.     Reflex  duller  in  di- 
rect proportion  to  the  degree  of  M. 

§  140.  There  is  one  objection  to  this  examination  when  made 
with  the  concave  mirror,  namely,  that  by  it  we  are  not  able  to 
distinguish  between  emmetropia  and  low  degrees  of  hyperme- 
tropia and  myopia,  since  in  them  all  the  shadow  moves  against 
the  mirror.  This  is  due  to  the  fact  that  the  source  of  illumina- 
tion, F1,  is  always  at  a  finite  distance  and  gives'  out  divergent 
rays,  and  if  it  is  situated  at  a  greater  distance  from  P  than  one 
meter,  only  a  limited  number  of  its  rays  will  enter  the  eye,  and 


DIAGNOSIS  OF  AMETROPIA  BY  THE    SHADOW-TEST. 

the  illumination  of  the  retinal  image  will  be  greatly  diminished. 
This  nearness  of  F1  to  P  necessitates  a  near  approach  of  0  to 
P.  As  a  consequence  of  this,  in  all  cases  of  M,  where  the  far 
point  lies  behind  0,  no  actual  inverted  image  of  F2  is  formed  in 
front  of  0,  but  on  the  contrary,  it  tends  to  become  virtual  and 
erect  and  is  classed  with  E.  and  H.,  and  has  the  same  move- 
ment against  the  mirror. 

In  order  to  obviate  this  and  have  sharply  defined  diagnostic 
movements  of  the  shadow,  Story  and  others  have  suggested  the 
use  of  a  plane  mirror,  which  would  enable  the  observer  to 
place  himself  at  a  distance  of  12  feet  or  more  from  P.  Under 
these  circumstances  the  rays  coming  from  the  flame  two  feet 
behind  P  and  fourteen  feet  from  the  mirror  would  approach 
parallelism  and  would  be  so  reflected  by  the  plane  mirror  into 
the  eye  P,  without  loss  by  dispersion.  On  emerging,  the  rays 
from  F2  could  form  a  real  image  six  feet  from  P  which  would  be 
recognized  by  0  and  a  M.  of  o  5  D  distinguished.  When  the 
plane  mirror  is  used,  however,  it  must  be  borne  in  mind  that 
the  movements  of  the  shadow  are  the  reverse  of  those  observed 
when  the  concave  mirror  is  used  ;  that  is,  in  H  and  E,  it  moves 
with  the  mirror,  in  M  against  it. 

The  reason  for  this  is  as  follows  :  When  the  concave  mirror 
is  used,  the  source  of  illumination  is  an  image  of  the  flame 
at  the  focus  of  the  mirror,  and  when  the  mirror  rotates  from 
right  to  left  this  image  also  moves  from  right  to  left,  and  con- 
sequently the  retinal  image  F2  moves  in  the  contrary  direction, 
with  the  results  as  we  have  seen.  With  the  plane  mirror,  how- 
ever, the  object  furnishing  the  light  is  a  virtual  erect  image  of 
.F  situated  as  far  behind  Mas  the  flame  F  is  in  front  of  it.  When 
the  mirror  is  rotated,  therefore,  from  right  to  left,  this  image 
moves  in  a  contrary  direction  and  its  retinal  image,  F2,  in  the 
same  direction  as  the  mirror.  The  image  furnished  by  F2  must 
move,  in  accordance  with  this,  in  a  direction  relative  to  the  mir- 
ror exactly  the  opposite  to  that  followed  in  the  examination 
with  the  concave  mirror. 

§  141.  The  examination  so  far,  however,  has  furnished  us 
with  no  definite  information  as  to  the  amount  of  ametropia. 


I2O  DIAGNOSIS  OF  AMETROPIA  BY  THE   SHADOW-TEST. 

We  can  know  the  higher  degrees  of  M.  or  H.,  and  if  the 
plane  mirror  is  used  even  the  lower  degrees,  but  we  can  only 
estimate  the  amount  of  departure  from  the  normal  optical  con- 
dition in  a  rough  manner  by  the  greater  or  less  dulness  of  the 
pupillary  reflex,  and  the  greater  or  less  extent  of  shadow 
movement. 

It  is  possible,  however,  to  obtain  a  quite  accurate  diagnosis 
by  this  method,  by  placing  in  front  of  the  eye  under  examina- 
tion correcting  glasses  in  succession  until  one  is  found  with 
which  emmetropic  movements  of  the  shadow  are  found. 

Let  there  be,  for  example,  a  short  movement  with  the  con- 
cave mirror  and  a  dull  reflex.  This  indicates,  of  course,  M., 
and  experience  teaches  us,  of  a  moderate  degree.  We  then 
put  a  — 4.  D  in  a  trial  frame,  and  placing  it  before  the  eye,  make 
another  observation  and  note  the  direction  of  the  shadow.  It 
is  found  to  still  be  with  the  mirror:  the  M.  is  under-corrected. 
After  trying  — 4.5  with  the  same  result  we  find  that  with  — 5 
there  is  large  movement  against  the  mirror,  and  a  maximum 
brightness  of  reflex.  This  shows  that  there  is  a  small  amount 
of  M.  (about  0.5  D)  remaining  uncorrected.  Adding  this  to 
the  5  D  we  have  5.5  D  as  about  the  degree  of  M.  present. 
Should  the  plane  mirror  be  used,  we  find  before  correction  a 
movement  against  the  mirror,  and  not  until  — 5.5  is  placed  in 
the  frame  do  we  find  a  movement  with  the  mirror. 

When  one  becomes  skilful  in  the  use  of  this  method 
an  approximation  to  within  I  D  of  the  optical  state 
of  the  eye  can  be  made  in  the  majority  of  cases.  For 
its  most  satisfactory  employment  a  wide  pupil  is  essential,  and 
it  is  necessary  that  the  eye  examined  shall  be  protected  thor- 
oughly from  all  light  except  that  which  comes  from  the  mirror. 

Like  most  of  the  other  methods  of  objective  examination, 
it  requires  much  practice  to  become  expert  in  its  use,  and  is, 
according  to  my  experience,  more  consumptive  of  time  than 
the  ordinary  ophthalmoscopic  methods. 

§  142.  It  will  be  seen  at  once  how  easy  it  is  to  use  this  meth- 
od in  the  diagnosis  of  astigmatism.  We  have,  for  this  purpose, 
simply  to  determine,  in  accordance  with  the  principles  laid 


DIAGNOSIS  OF  ASTIGMATISM  BY  THE  SHADOW-TEST.          121 

down,  the  ametropia  of  the  principal  meridians  in  the  same 
way  that  we  examine  for  the  general  ametropia.  Moreover, 
the  direction  of  the  principal  meridians  is,  owing  to  some  pe- 
culiarities of  the  phenomena,  very  readily  discovered.  If  these 
meridians  stand  as  they  commonly  do,  vertically  and  horizon- 
tally, there  will  be  a  difference  in  the  amount  or  character  of 
shadow  movement  on  rotation  of  the  mirror  in  these  directions 
respectively.  But  should  the  meridians  lie  obliquely — one  be- 
ing, say,  at  45° — on  horizontal  movement  of  the  mirror,  the 

Fig.  36. 


DIAGRAM  SHOWING  How  THE  SHADOW  IN  SKIASCOPY  MOVES  ACROSS  THE  PUPIL 
WHEN  THE  MERIDIANS  IN  ASTIGMATISM  ARE  OBLIQUE. 

shadow  does  not  move  in  a  horizontal  direction,  but  at  an  angle 
of  45°,  and  for  the  following  reasons: 

We  know,  from  the  facts  demonstrated  in  Chapter  II,  that 
both  the  diffuse  retinal  image  of  Fl  and  the  image  of  this  im- 
age'as  seen  by  the  observer,  0,  being  formed  by  an  astigmatic 
system  are  not  circular  as  in  general  ametropia,  but  oval, with  the 
long  diameter  in  the  direction  of  one  of  the  principal  meridians. 
The  oval  lying,  as  it  does  in  our  supposed  case,  with  its  long 
axis  at  45°,  advances,  when  the  image  as  a  whole  moves  hori- 
zontally, its  shadowy  edge  in  a  direction  at  right  angles  to  its 
axis.  Without  going  into  any  mathematical  demonstration  of 


122  DIAGNOSIS  OF  ASTIGMATISM  BY  THE  SHADOW-TEST. 

the  matter  it  is  easy  to  convince  oneself  of  this  fact  by  a  very 
simple  experiment.  Take  a  circular  opening  (Fig.  36)  and 
place  behind  it  an  object  with  a  straight  edge  a  c  at  an  angle 
of  45°.  Now  advance  this  object  in  a  strictly  horizontal  direc- 
tion to  b  d;  the  apparent  movement  of  the  object  will  be,  not 
from  a  to  b  and  c  to  d,  but  in  the  direction  of  the  line  e /per- 
pendicular to  a  c. 

§  143.  In  examining  for  astigmatism  by  means  of  the 
"  shadow  test "  we  first  throw  the  light  into  the  eye  in  the  usual 
manner,  and  rotating  the  mirror  in  various  directions  note  the 
brightness  of  the  reflex,  and  the  direction  and  extent  of  the 
shadow  movements.  If  astigmatism  is  present,  it  reveals  itself  at 
once  by  the  incongruity  of  movement  explained  in  the  preced- 
ing paragraphs,  and  the  direction  of  the  principal  meridians  is 
thus  indicated.  We  then  proceed  to  test  the  refraction  of  each 
meridian  separately  by  placing  in  the  trial  frame  before  the  eye 
various  correcting  glasses  and  rotating  the  mirror  in  the  direc- 
tion of  this  meridian  until  one  lens  is  found  which  gives  emme- 
tropic  motions.  The  meridian  at  right  angles  to  this  is  then 
taken  and  the  refraction  determined  in  the  same  manner* 
Knowing  then  the  refraction  in  the  two  meridians  it  is  easy, 
in  the  way  already  sufficiently  dwelt  upon,  to  find  the  amount 
of  astigmatism.  When  the  correcting  glasses  thus  indicated  are 
placed  in  the  frames  with  the  axes  of  the  cylinders  at  the 
proper  angle,  movements  of  the  mirror  in  all  directions  should 
give  emmetropic  motions  to  the  shadows. 

BIBLIOGRAPHY. 


Baker,  A.  R. — Retinoscopy.    Amer.  Jr.  Ophth.  I.     Pp.  116-19.     1884. 

Charnley,  W. — On  the  theory  of  the  so-called  keratoscopy  and  its  practical  appli- 
cation. Roy.  Lond.  Ophth.  Rep.  X.  P.  344. 

ChiberL — Determin.  quantitat  de  la  myop.  par  la  keratoscopie  (fantoscopie  nitin.) 
a  1'aide  de  un  simpl.  mirror  plan.  Ann.  d'oculist.  LXXXVIII,  P.  238.  1882. 

Cuignet — Keratoscopie.  Recuiel  d'  oph.     1873.     Pp.  14  and  316.", 

Cuignet — Astig.  comp.  et  obliq.:  keratoscopie.  Rec.  d'ophth.  35.  I.  Pp.  73-5. 
Paris.  1879. 

Cuignet — Apropos  de  keratoscopie.     Rec.  d'ophth.     P.  321.     1880. 

Forbes,  L. — On  keratoscopy.    Ophth.  Hosp.  Rep.    X.    P.  62.     1880. 


BIBLIOGRAPHY.  123 

Hubert  et  Prouff— Keratoscopie.     Rev.  Clin.  d'Oculist.    No.  5.    P.  no.     1884. 

Hartridge,  G. — The  refraction  of  the  eye.    2nd  edition.    London,  1886. 

Jackson,  Edward — The  measurement  of  Refraction  by  the  shadow-test,  or  Retino- 
scopy.  Amer.  Jnl.  Med.  Sci.  April,  1885. 

Juler — The  applicat.  of  retinoscopy  to  the  diag.  and  treat,  of  the  errors  of  refract. 
Brit.  Med.  Jr.  Pp.  116-70.  1882. 

Mengin — De  la  keratoscopie  comme  moyen  de  diagnostic  des  differt.  etats  ametrop. 
de  1'oeil.  Rec.  d'ophth.  P.  122.  1878. 

Morton,  A.  Stanford. — Refraction  of  the  eye,  its  diagnosis  and  the  correction  of  its 
errors  with  a  chapter  on  Keratoscopy.  London,  1881. 

Morton,  A.  S.  and  Barrett,  J.  W. — A  clinical  investigation  of  the  various  methods 
of  practising  retinoscopy.  Brit.  Med.  Jnl.  Jan.  1 6,  1886. 

Parent  de  la  keratoscopie.    Rec.  d'ophth.    P.  65.    1880. 

Parent— Diagnost.  et  determ.  object,  de  1'astig.  Rec.  d'Ophth.  35.  III.  Pp. 
229-52.  1881. 

Story,  J.  B. — The  advantages  of  the  plane  ophth.  mirror  in  retinoscopy.  Ophth. 
Review.  II.  P.  228. 


CHAPTER    IX. 


KERATOMETRY  AND  KERATOSCOPY. 

§  144.  The  fresh  impulse  given  to  the  study  of  astigmatism 
in  recent  times  was  by  measurements  of  the  cornea  in  its  vari- 
ous meridians,  first  made  systematically  by  Knapp.  And  since 
the  cornea  has  been  found  to  play  the  chief  part  in  the  anomaly, 
the  most  convenient  and  proper  method  of  investigation  would 
seem  to  be  by  some  kind  of  keratometry.  And  so  it  would  be 
but  for  the  fact  that,  until  very  recently,  no  rapid  and  accurate 
method  of  keratometry  has  been  at  the  command  of  the  prac- 
titioner. The  ophthalmometer  of  Helmholtz  is  cumbersome, 
expensive,  difficult  to  handle  and  very  consuming  of  time ;  all 
of  which  tend  to  exclude  it  from  the  consultation  room. 

§  145.  The  desirability  of  some  practical  method  of  kera- 
tometry being  recognized,  several  attempts  have  been  made  to 
realize  it,  but  up  to  1881  none  had  been  presented  which  offered 
theonerits  of  accuracy,  facility  of  handling,  simplicity  of  struc- 
ture and  comparative  cheapness.  In  that  year,  Javal  exhibited 
before  the  International  Medical  Congress,  at  London,  an  in- 
strument constructed  by  himself  in  conjunction  with  Shiotz 
which  fulfilled  all  these  requirements,  and  in  my  estimation 
must  be  regarded  as  the  most  important,  practical  and  exact 
means  of  diagnosis  given  to  our  science  since  the  invention  of 
the  ophthalmoscope. 

§  146.  As  regards  the  designation  of  this  method  of  examin- 
ation we  think  the  name  "keratometry"  more  accurately  descrip- 
tive than  "ophthalmometry."  The  latter  term  could  be  applied 
to  measurements  of  the  eye  in  any  or  all  of  its  parts,  whereas, 
in  the  method  under  consideration,  we  simply  measure  the  ra- 
dius of  curvature  of  the  cornea  at  any  desired  locality.  Neither 
would  "  keratoscopy"  be  correct,  since  this  means  a  simple  in- 
spection of  the  cornea  and  does  not  necessarily  imply  any 

{124  > 


DIFFERENT  METHODS  OF  DETERMINING  THE  RADIUS.         12$ 

measurements;  a  term  quite  appropriate,  however,  to  the 
methods  of  Placido  and  DeWecker,  to  be  described  later. 

§  147.  The  instrument  of  Javal  and  Shiotz  1  is  constructed 
on  the  well-known  fact  that  the  image  of  an  object  of  a  certain 
size  at  a  fixed  distance  from  a  convex  reflecting  surface  grows 
smaller  as  the  radius  of  curvature  of  that  surface  becomes 
shorter. 

There  are  several  ways  in  which  this  principle  can  be  ap- 
plied in  determining  the  curvature  of  any  given  convex  sur- 
face. 

(a.)  A  certain  size  of  image  may  be  taken  as  a  standard  and  the 
distance  between  the  object  and  reflecting  surface  varied  until 
this  standard  size  of  the  image  is  reached.  It  can  then  be  de- 
termined, by  calculation,  what  changes  in  radius  of  curvature 
correspond  to  a  certain  variations  in  distance ;  or 

(b.}  the  distance  separating  the  object  and  reflecting  sur- 
face may  remain  the  same  while  the  size  of  the  object  is  varied 
till  the  standard  size  of  image  is  obtained ;  or 

(c.)  the  distance  and  size  of  object  being  fixed  the  calcu- 
lation may  be  based  upon  the  varying  size  of  the  image. 

§  148.  Of  these  plans  the  first  and  second  are  the  most 
available,  and  of  the  two,  Javal  and  Shiotz  have  chosen  the 
second. 

The  essential  part  of  the  instrument  for  ordinary  use  is  a 
Wollaston's  bi-refringent  prism  of  such  a  power  that  it  shall 
give  an  exact  doubling  of  an  object  3  mm  in  diameter  when  it 
is  at  27  cm  from  the  prism ;  or,  expressed  in  another  way,when 
the  object  is  27  cm  from  the  prism  and  the  edges  of  the  double 
images  touch,  the  diameter  of  the  object  must  be  3  mm.  The 
object  to  be  measured  in  this  case  is  the  corneal  reflection  of 
some  suitable  object  placed  in  front  of  the  eye. 

The  accessories  of  the  instrument  are  the  optical  appliances 
for  seeing  this  double  image  to  the  best  advantage  and  from  a 
convenient  distance,and  a  means  for  measuring  the  varying  size 
of  the  object  which  furnishes  the  corneal  image. 

1  Made  by  M.  Laurent,  rue  de  1'Odeon,  Paris.  The  net  price  of  the  instrument  is 
350  francs.  It  can  be  obtained  through  J.  W.  Queen  &  Co.,  Philadelphia. 


126       CONSTRUCTION  OF  JAVAL  AND  SCHIOETZ  INSTRUMENT. 

In  the  construction  of  the  objective  W  (Fig.  37)  the  birefrin- 
gent  prism  is  placed  between  two  convex  lenses  having  each  a 
focus  of  27  cm.  At  the  focus  of  the  second  lens,  found  between 
E  and  0,  a  fine  spider's  web  is  stretched  across  the  tube.  By 

Fig.  37- 


THE  OPHTHALMOMETER  (KERATOMETER)  OF  JAVAL  AND  SCHIOETZ. 

means  of  these  two  lenses  and  the  prism  an  inverted  double  im- 
age of  the  reflection  from  the  cornea,  which  is  situated  27  cm 
from  the  first  lens,  is  formed  at  the  spider's  web,  and  this  double 
image  is  seen  through  the  ocular  0  whose  focus  also  lies  at  the 
spider's  web.  This  double  image  is  seen  clearly,  only  when  the 
eye  of  the  observer  is'  accurately  adjusted  by  means  of  the 
ocular  to  that  distance.  This  inverted  double  image  of  the 
corneal  reflection  is  not  magnified.  The  reflection  and  its  im- 
age are  at  conjugate  foci,  and  the  distance  of  the  cornea  from 
the  first  lens  being  the  same  as  the  distance  of  the  spider's  web 


CONSTRUCTION  OF  JAVAL  AND  SCHIOETZ  INSTRUMENT.        I2/ 

from  the  second  lens,  the  two  images  must  be  of  the  same  size  ; 
in  other  words,  the  reflection  image  is  simply  transferred  from 
the  cornea  to  the  focus  of  the  ocular. 

The  only  thing  now  needed  to  furnish  the  necessary  means 
for  an  examination  is  an  object  whose  size  can  be  regulated  at 
will.  All  that  is  essential  of  such  an  object  are  two  opposing 
sides,  in  order  that  we  may  know  when  the  edges  of  the  dou- 
ble images  are  in  contact.  This  is  obtained  by  having  two 
white  bands  MM'  moveable  on  an  arc  A,  that  is  fixed  on  the 
tube  Wat  about  35  cm.  from  the  cornea  which  serves  as  its 
center  of  curvature.  The  outer  edges  of  these  two  bands  con- 
,  stitute  the  lateral  limits  of  the  object.  As  these  bands  are 
moveable  it  is  easy  to  form  an  object  of  any  desired  size  which 
can  be  accurately  measured  on  the  arc. 

The  instrument  has  now  only  to  be  properly  mounted  to  be 
ready  for  use,  and  the  manner  in  which  this  is  done  is  well 
shown  in  Fig.  37. 

§  149.  In  making  an  examination  the  head  of  the  examinee  is 
placed  in  the  head  rest  and  the  eye  not  to  be  examined  is  cov- 
ered with  the  shade  P.  The  optical  part  of  the  apparatus  is 
moveable,  as  a  whole,  backwards,  forwards  and  laterally  on  the 
foundation  board,  and  the  elevation  of  the  tube  is  regulated  by 
the  thumbscrew  V. 

The  ocular  O  must  first  be  accurately  adapted  to  the  spider's 
web  for  the  eye  of  each  observer.  The  tube  is  then  brought 
into  line  with  the  cornea  and  by  movements  back  and  forth  so 
adjusted  that  a  clearly  defined  double  image  of  MM'  shall  be 
formed  at  the  spider's  web,  where  it  is  seen  by  the  observer 
through  the  ocular  0.  When  this  is  done  the  prism  is  27  cm. 
from  the  cornea,  and  when  the  double  images  of  the  corneal 
reflection  formed  by  it  touch  by  their  opposing  edges,  each  im- 
age has  a  diameter  of  3  mm. 

When  the  instrument  is  thus  adj  usted,  one  of  the  white  bands  is 
moved  along  the  arc  until  the  inner  edge  of  its  image,  as  seen 
through  the  ocular  0,  touches  the  outer  edge  of  the  image  of 
the  other  band.  Then,  as  stated  above,  the  diameter  of  the 
corneal  image  of  MM'  is  3  mm.  The  size  of  the  object  MM' 


128  LIMITATIONS  OF  THE  INSTRUMENT. 

can  then  be  measured  off  on  the  arc  A.  Knowing  now  the 
size  of  the  object,  the  size  of  the  image  and  the  distance  sep- 
arating the  object  from  the  reflecting  surface,  we  have  all  the 
data  necessary  for  calculating  the  radius  of  curvature  of  the 
convex  surface  of  the  cornea. 

§  150.  Thus  far  the  instrument  has  no  special  practical  ad- 
vantage over  the  ophthalmometer  of  Helmholtz,  for  it  is  the 
coritplitations  from  the  observed  data  that  are  so  tedious  and 
time-consuming.  But  Javal  and  Shiotz  have  so  arranged  the 
various  parts  of  their  apparatus  that  a  certain  size  of  object 
when  the  instrument  is  properly  adjusted  shall  correspond  to  a 
certain  radius  of  curvature,  which  can  be  read  off  on  the  arc 
in  millimetres  or  expressed  in  refracting  power  by  dioptrics. 
A  variation  of  6  mm.  in  the  size  of  the  object  35  cm  from  the 
cornea  corresponds  to  a  change  of  I  D  in  refracting  power  and 
a  variation  of  36  mm.  in  size  (6  D)  corresponds  to  a  difference 
of  about  i  mm.  in  the  length  of  the  radius  of  curvature.  As 
it  is  comparatively  easy  by  this  instrument  to  approach  to  with- 
in 0.25  D  of  the  actual  refracting  power,  an  estimation  of  the 
radius  of  curvature  is  possible  up  to  l/,0  mm.,  which  is  all  that 
could  be  demanded  in  the  practical  determination  of  refrac- 
tion. 

§  151.  As  it  is  not  possible  with  this  instrument  to  examine 
with  any  degree  of  accuracy  the  lenticular  surfaces,  and  as 
these  form  important  elements  in  the  general  optical  condition 
of  the  eye,  the  apparatus  is  of  limited  advantage  in  obtaining 
the  refraction  of  the  eye  as  a  whole,  except  in  cases  of 
aphakia.  Its  usefulness  for  estimating  general  ametropia  is 
still  further  diminished  by  the  fact,  which  the  instrument  itself 
has  done  so  much  to  establish,  that  the  conditions  of  myopia 
and  hypermetropia  are  not  due,  except  in  rare  instances,  to 
variations  in  the  refracting  surfaces  of  the  eye,  but  to  changes 
in  the  antero-posterior  diameter  of  the  eye-ball. 

§  152.  Since,  however,  it  is  a  fact  demonstrated  more  than 
twenty  years  ago  in  the  physiological  laboratory,  and  now  fully 
corroborated  by  this  very  instrument  in  the  consultation  room, 
that  the  much  larger  part  of  astigmatism  is  corneal,  and  since 


METHOD  OF  USING  THE  INSTRUMENT.  1 29 

it  is  as  easy  with  it  to  measure  the  cornea  in  one  meridian  as 
in  another,  the  value  of  this  keratometer  in  the  diagnosis  of 
astigmatism  can  hardly  be  over-estimated.  In  fact,  it  might 
with  great  propriety  be  called  an  "astigmometer." 

The  tube  W  can  be  turned  on  its  axis,  carrying  with  it  the 
arc  and  the  white  bands  MM',  and  any  departure  from  its  in- 
itial position  is  shown  by  a  pointer  moving  over  the  fixed  grad- 
uated disk  E.  It  thus  becomes  possible  to  measure  the  cor- 
neal  curvature  in  any  desired  meridian  and  to  know  the  exact 
direction  of  that  meridian.  We  have,  therefore,  only  to  meas- 
ure the  cornea  in  the  manner  above  described  in  its  various 
meridians,  read  off  on  the  arc  the  radius  of  each  and  take  the 
difference  between  the  strongest  and  weakest  in  order  to  have 
the  amount  of  astigmatism  expressed  in  difference  in  radius 
(r)  or  in  dioptrics. 

The  inventors  have  facilitated  this  determination  in  a  most 
ingenious  manner,  whereby  it  is  possible  to  see  in  the  double 
image  itself,  and  without  the  necessity  of  reading  on  the  arc, 
the  difference  in  the  refraction  of  the  principal  meridians.  One 
of  the  sides  of  the  band  M,  instead  of  being  straight  is  made 
in  the  form  of  five  equal  steps,  as  shown  in  A,  Fig.  38.  It  is 
the  lateral  edge  of  the  lower  step  which  must  be  brought  in 
contact  with  the  edge  of  the  other  band  M'  in  order  to  have 
the  image  of  the  required  size  of  3mm. 

§  153.  In  making  examinations  with  the  instrument  for  as- 
tigmatism the  tube  is  turned  on  its  axis  and  the  band  M' 
moved  on  the  arc,  ^"remaining  stationary,  until  one  meridian 
is  found  in  which  the  bases  of  the  two  bands  form  a  continuous 
line,  when  their  sides  are  in  contact.  The  refraction  of  the 
cornea  in  this  meridian  (indicated  by  the  pointer  on  the  disk 
E)  is  then  read  off  on  the  arc  in  r  or  in  dioptrics  and  noted. 
The  tube,  with  the  arc,  is  then  rotated  to  the  opposing  merid- 
ian, when  it  will  be  found,  should  astigmatism  be  present,  that 
the  sides  have  either  separated  or  overlapped.  If  they  have 
overlapped,  the  amount  of  crossing  is  shown  by  the  number  and 
portions  of  the  steps  of  M  covered  by  M',  which  is  readily  rec- 
ognized by  the  fact  that  these  steps  and  parts  of  steps  are  just 


I3O  METHOD    OF   USING    THE    INSTRUMENT. 

twice  as  bright  (for  obvious  reasons)  as  the  remaining  steps  of 
the  band.  Now,  the  size  of  these  steps  has  been  so  regulated 
that  each  one  shall  represent  I  D  of  refracting  power.  If, 
therefore,  one  of  these  steps  is  covered,  there  is  a  difference  of 
I  D  in  the  two  meridians ;  if  two  are  covered  (B,  Fig.  38)  we 

fig.  38. 


APPEARANCE  OF  THE  CORNEAL  IMAGE  OF  THE  BANDS  IN  THE  KERATOM- 
ETER  WHEN  THERE  IS  A  DIFFERENCE  IN  THE  REFRACTION  IN  THE  T\VO  MKKIDIANS 
OF  THE  CORNEA. — A,  meridian  of  greatest  curvature  ;  B,  the  meridian  of  least  curva- 
ture (longest  radius). 

know  the  difference  is  2  D  and  the  necessity  of  reading  the 
difference  on  the  arc  is  obviated.  If,  however,  it  is  desired  to 
know  the  radius  of  curvature  exactly  in  this  meridian,  indica- 
ted by  the  pointer  on  the  disk  E,  the  band  M'  is  moved  on  the 
arc  until  its  edge  is  just  in  contact  with  the  lower  step  of  the 
graded  band  M.  Its  position  on  the  arc  will  then  give  the  de- 
sired information. 

Moreover,  the  meridian  in  which  there  is  a  crossing  of  the 
bands  is  the  less  refracting.  The  fact  of  the  two  images  over- 
lapping shows  that  they  have  a  diameter  greater  than  3  mm. 
and  consequently  the  surface  giving  them  must  have  less  cur- 
vature than  that  giving  them  with  edges  in  contact,  and  in  or- 
der to  have  them  thus  in  contact  the  object  must  be  made 
smaller  by  moving  M'  on  the  arc  towards  M.  If  the  images 
of  the  bands  separate  in  moving  the  arc  from  its  initial  position 


ITS    LIMITATIONS.  13! 

where  they  were  in  contact,  it  shows  that  the  first  meridian  is 
the  less  refracting  with  a  larger  radius  of  curvature.  The  cur- 
vature of  the  meridian  where  the  separation  is  greatest  is  de- 
termined by  moving  the  band  M'  along  the  arc  away  from  M 
until  the  edges  again  touch.  The  refraction  can  then  either  be 
read  off  on  the  arc  and  the  difference  taken  between  that  and 
that  of  the  other  meridian,  or  the  arc  can  be  turned  again  to  the 
opposing  and  less  refracting  meridian,  when  the  number  and 
parts  of  steps  overlapping  will  show  at  once  the  difference  be- 
tween the  two  meridians,  expressed  in  dioptrics  and  fractions 
thereof. 

§  154.  We  have  now  ascertained  the  amount  of  the  astigma- 
tism and  the  direction  of  the  meridians  of  greatest  and  least 
refraction,  but  the  data  furnish  no  clue  as  to  the  form  of  the 
anomaly.  The  measurements  give  no  information  as  to  wheth- 
er the  astigmatism  is  simple  or  compound,  myopic  or  hyperme- 
tropic,  or  mixed.  When,  for  instance,  the  horizontal  meridian 
is  found  to  be  least  refracting,  it  may  be  that  (a)  it  is  emmetro- 
pic,  while  the  vertical  meridian  is  myopic — simple  M.  astig.;  or 
(fr)  it  may  be  myopic  also  but  less  so  than  the  vertical — comp. 
M.  astig ;  or  (c]  it  may  be  hypermetropic,  the  vertical  being 
emmetropic — H.  astig ;  or  (d]  it  may  be  that  both  meridians 
are  hypermetropic,  this  one  being  more  so — Comp.  H.  astig.;  or 
(e)  it  may  be  hypermetropic  while  the  other  is  myopic — mixed 
astig.  The  differential  diagnosis  of  the  form  must  therefore 
be  made  by  some  of  the  other  methods  of  examination. 

The  only  other  defect  of  the  method  is  that  it  leaves  us  in 
ignorance  of  the  amount  of  the  lenticular  astigmatism.  One 
important  fact  has  been  developed  by  the  use  of  the  instrument 
in  this  connection  and  that  is  that  in  at  least  one  half  the  cases 
it  is  neutralizing  in  its  character.  When  the  individual  is  be- 
yond 40  years  of  age,  however,  it  is  rare  to  find  any  important 
difference  between  the  total  and  the  corneal  astigmatism. 

In  the  following  table  are  recorded  15  cases  taken  as  they 
came  from  my  note-book  showing  the  difference  between  the 
astigmatism  as  determined  by  glasses  and  that  found  on  meas- 


132      DIFFERENCE   BETWEEN    CORNEAL    AND   TOTAL  ASTIGMATISM. 

urement  of  the  cornea.  The  excess  of  corneal  refraction  is  des- 
ignated by  -f,  the  deficiency  by  — . 

TABLE  VI. 


No. 

Name. 

Age. 

Astig.  by  Glasses 

Astig.      by 
Keratome- 
ter. 

Difference. 

i 

Mr.  N. 

48 

L  I 
Rl.S 

I 
i-5 

2 

Mrs.  H. 

50 

Li.5 
Ri 

'•5 
i. 

3 

Mrs.  C. 

52 

L2 
R2 

2-5 

2-5 

+0.5 

4 

Mrs.  M. 

21 

£4 

Ri-5 

4- 
'•25 

—  0.25 

5 

Miss  S. 

28 

L  1.25 
K3 

1.25 

3-25 

-0.25 

6 

Miss  C. 

17 

Lo-5 

0.75 

-0.25 

7 

Mrs.  M. 

38 

Ri.25 

1.25 

8 

Mr.  L. 

'9 

K  0.5 

nil 

-0.5 

9 

Mr.  G. 

8 

Ro 

0.5 

+0.5 

10 

Miss  G. 

,8 

Ro-5 

0.5 

it 

Miss  C. 

36 

L3 
*3 

3-25 
3-25 

+0.25 
+0.25 

12 

Mr.  G. 

5° 

L4-S 
K4-S 

4- 
4-25 

—0.5 
—  0.25 

'3 

Miss  L. 

18 

L  none 
Ko-5 

0.5 
i. 

-0.5 
+0.5 

H 

Mrs.  C. 

33 

L3 
R4-5 

3- 
4- 

—0.5 

'5 

Mr.  M. 

27 

L  none 
R  0.25 

0.5 
1-25 

-0.5 

+  1- 

These  cases  well  represent  the  average  of  my  examinations 
by  this  instrument  which  now  number  more  than  100.     I  have 


PLACIDO  S    KERATOSCOPE.  133 

never  found  a  greater  difference  than  iD,  and  the  direction  of 
the  principal  meridians  has  always  been  found  to  correspond 
essentially  with  the  corneal  meridians  as  determined  by  the 
keratometer. 

§  155.  The  apparatus,  for  its  most  satisfactory  employment, 
requires  a  good  illumination  of  the  white  bands.  I  find  that  in 
this  climate  the  light  from  an  unobstructed  window  is  quite 
sufficient.  But  for  dark  days  and  consultation  rooms  not  well 
lighted,  the  instrument  is  provided  with  argand  gas-burners  and 
reflectors  which  make  it  possible  to  use  it  under  all  circum- 
stances. 

39- 


THE  KERATOSCOPE  OF  PLACIDO. 

§  156.  PLACIDO'S  KERATOSCOPE.  In  1880  Placido,  of  Porto,  de- 
scribed an  instrument  for  noting  changes  in  the  form  of  the 
cornea  by  means  of  the  reflection  from  its  surface  of  a  series  of 
concentric  circles.  This  is  the  simplest  form  of  keratoscopy 
and  is  available  to  any  one  at  the  cost  of  very  little  trouble. 
Take  a  board  of  any  inflexible  material — wood,  sheet-iron  or 
stiff  paper — 25  or  30  cm.  square,  and  draw  on  its  white  surface  5 


134  ITS    VALUE   IN    REGULAR   ASTIGMATISM. 

concentric  black  circular  bands  I  cm  in  width  and  1^2  cm. 
apart  from  each  other  (Fig.  39).  Make  a  hole  in  the  center  of 
the  disk  through  which  to  look,  and  you  have  all  the  essential 
parts  of  the  instrument.  The  patient  is  to  be  placed  with  the 
back  to  a  good  light  and  the  board  held  at  right  angles  to 
the  visual  axis  at  from  8  to  12  inches  from  the  eye  under  ob- 
servation. If  there  is  no  astigmatism,  the  reflex  from  the  apex 
of  the  cornea  is  circular  and  there  is  no  irregularity  in  the 
course  of  the  circles.  Should  regular  astigmatism  be  present, 
the  corneal  reflex  will  be  oval  with  its  long  diameter  in  the  di- 
rection of  the  meridian  of  least  refraction.  For  the  purpose  of 
enlarging  the  image,  as  well  as  for  relieving  the  accommoda- 
tion of  the  observer  a  convex  lens  can  be  placed  behind  the 
hole  in  the  disk. 

§  157.  Javal  has  added  one  of  these  disks  to  his  ophthalmo- 
meter.  The  principal  value  of  this  disk  is,  as  we'shall  see,  in 
examining  for  irregular  astigmatism.  It  is  of  comparatively 
little  use  in  the  determination  of  the  regular  forms.  At  least 
I,  after  considerable  experimentation  with  it,  have  not  been 
able  to  satisfy  myself  of  the  existence  of  astig.  below  3D.  The 
variation  between  the  meridians  of  least  and  greatest  refraction 
is  represented,  as  Javal's  instrument  shows,  by  a  difference  in 
radius  of  curvature  of  about  */«  of  a  millimeter  for  one  dioptre  of 
refracting  power.  It  requires  a  most  expert  eye,  to  detect  in 
the  corneal  reflection  a  difference  of  l/3  of  a  millimeter  in  the 
radii  of  two  opposing  meridians,  as  expressed  by  the  departure 
of  the  figure  from  a  strict  circle.  For  a  simple  rough  estimation 
of  the  higher  degrees  it  is,  however,  of  some  value,  particularly 
in  the  way  Javal  has  adapted  it  to  his  instrument. 


DE  WECKER'S  SQUARE. 
Fig.  40. 


135 


WECKER'S  SQUARE  FOR  TESTING  FOR  CHANGES  IN  CORNEAL  CURVATURE. 

Fig.  41. 


FIGURES  FOR  DETERMINING  THE  AMOUNT  OF  CHANGE  IN  THE  CORNEAL  REFLEC- 
TION OF  WECKER'S  SQUARE. 


136  THE    FINAL   TEST    OF    DIAGNOSIS. 

§  1 58.  The  same  may  be  said  in  a  general  way  of  De  Wecker's 
modification  of  Placido's  idea.  This  consists  of  a  square  in- 
stead of  a  circle  (Fig.  40)  whose  cornea!  image  is  to  be  ob- 
served. He  has  made  an  addition  to  the  method  in  furnishing 
a  standard  of  comparison  for  the  corneal  image  of  the  square 
by  placing  on  a  black  surface  (Fig.  41)  the  parallelograms  which 
correspond  to  the  different  degrees  of  astigmatism  expressed 
in  dioptrics.  This  is  held  near  the  eye  under  observation 
and  a  direct  and  simultaneous  contrast  of  the  two  outlines  is 
thus  furnished,  which  enables  the  observer  to  judge  the  more 
readily  as  to  whether  there  has  been  any  departure  from  the 
strict  form  of  the  square  and,  if  so,  to  estimate  roughly  how 
much. 

§  159.  We  have  now  completed  a  description  of  all  the  im- 
portant methods  for  the  diagnosis  of  astigmatism.  Some,  it 
has  been  seen,  have  an  advantage  in  one  particular  and  some 
in  another,  while  all  have  certain  insufficiencies.  A  preference 
for  one  over  the  other  will  generally  be  due  to  the  fact  that 
the  individual  has  practiced  it  more  assiduously  than  the  rest 
and  thereby  attained  greater  skill  in  its  use. 

§  1 60.  But  no  one  method  should  be  relied  upon  exclusively;  and 
no  diagnosis  of  astigmatism  should  be  considered  as  fixed  until  it 
has  been  verified  by  an  examination  with  cylindrical  glasses  and 
test-types  as  described  in  Chapter  III.  The  highest  visual  acute- 
ness  must  always  be  the  final  test  of  a  diagnosis. 

BIBLIOGRAPHY. 


Angelucci,  A. — Sulla  refrazione  e  correzione  della  cornee  coniche  ed  ectatiche. 
Ann.  d.OtL  XIII.  Fas.  I.  P.  35. 

Astigmometrie  dc  DeWecker  et  Masselon.  Ann.  d'  Oculist.  LXXXVIII.  Pp. 
44-6.  1882. 

Berger — Ein  modifict  Keratoskop.    Wien.  Med.  Presse.     No.  46.     1882. 

Berger — Ueber  d.  Diag.  d.  Kriimmungsanom.  d.  Homhaut  mil  d.  Keratoskop. 
Wien.  Med.  Wchnschft.  No.  51.  1882. 

Berger — Der  Hornhautspiegel  (Keratoskop)  u.  seine  pract  Anwendung.  Deutsch. 
Med.  Ztg.  Hft.  6,  1884. 

Bergmeister — Demonst  d.  Keratskops  v.  Placido.  Anzeig  d  k.  k.  Gesellsch.  d. 
Aertz  in  Wien.  No.  2.  1882. 


BIBLIOGRAPHY.  137 

Berlin,  E.— Zur  Berech.  d.  Astig  d.  Hornhaut  Klin  Monatsbl.  f.  Augenhlk.  IX. 
Pp.  217-9.  1871. 

Burnett,  Swan  M. — Ophthalmometry  with  the  ophthalmometer  of  Javal  and 
Schiotz,  with  an  account  of  a  case  of  keratoconus.  Archives  of  Oph.  XIV.  Pp. 
169-176. 

Fonseca — Astigmatoscope.    Arch.  Ophth.  de  Lisbon.    Jan.-Feb.     1882. 

Gavarret— Astig.  et  Ophtalmom6trie.  Rev.  Scient.  XXX.  Pp.  74-80.  Paris. 
1882. 

Hasner — Ueber  Placidos  Keratoskop.    Prg.  Med.  WchnschrfL    No.  13.     1882. 

Hirschberg — Das  stabile  Keratoscop.     Centralbl.  f.  Augenhlk.     P.  30.     1883. 

Javal  et  Schiotz — Un  ophthalmometer  practique.  Ann.  d'Oculist  Juil.  Aout. 
1881. 

Javal — Contrb.  a  1'ophthalmomet.  Ann.  d'OculisL     Mai-Juni.     1882. 

Javal — Seconde  Contrib.  a  POphthalmomet.     Ann.    d'Oculist.    Jul.-Aout.     1882. 

Javal — Troisieme  Contrib.  a  1'ophthalmomet — Descpt.  de  quelques  images  kerato- 
scop.  Ann.  d'Oculist.  Jan.  Feb.  Mars.  1883. 

Javal — Quatrieme  Contrib.  a  1'ophthalmomet.    Ann.  d'Oculist     Sept.  Oct.     1883. 

Javal — Prioritats  Reklam.  beziiglich  des  Keratoscops.  Centbl.  f.  Augenheilk. 
1882.  P.  122. 

Landesberg— The  Keratoscop.     Phila,  Med.  Times.    XIII,    P.  784.     1883. 

Laqueur — Ueber  d.  Hornhautkriimmung  in  normalen  Zustande  u.  unter  pathol. 
Verhaltnissen,  ophthalmomet.  Untersuch.  Graefes  Arch.  XXX.  I.  Pp.  99-134. 

Leroy,  C.  J.  A. — De  la  Keratoscopie  ou  de  la  forme  de  la  surface  corneenne 
deduite  d.  images  apparentes  reflech.  par  elle.  Arch.  d'Ophth.  IV.  No.  2.  P. 
140.  1884. 

Mayerhausen — Notiz  zur  klin.  Veranschaulich.  d.  Winkels  y  (mittelst  d.  Keratos- 
kops.  Centralbl.  f.  Angenheilk.  1882.  P.  123. 

Montardit — Optometro-Astigmometro.     Revis.  d'Cienc.  Med.    Juli.     1881. 

Nordenson,  E. — Rech.  ophthalmomet  sur  Pastig.  de  la  cornee  chez  des  ecoliers 
de7a2oans.  Ann.  d'Oculist.  LXXXIX.  Pp.  110-38.  1883. 

Pfalz — Ophthalmometrische  Untersuchungen  u.  corneal-Astigmatismus  mit  dem 
ophthalmometer  von  Javal  u.  Schiotz,  etc.  Graefes  Archiv.  XXXI.  I.  Pp.  201-228. 

Placido — Astigmatoscope  explorateur.  Period  d.  oftal.  pract.  Sept.  Nov.  1880. 
Also  Centralbl.  f.  prakt.  Augenhlk.  VI.  P.  30. 

Placido — Nouv.  Instrument  de  esploracas  da  cornea ;  astigmatoscop.  explor.  advr. 
Period  de  ophth.  prat  II.  No.  r.  P.  30.  Lisb.  1881. 

Reich,  M. — Result,  einiger  ophthalmomet.  u.  mikro-optomet  Messungen.  Grae- 
fes Arch.  XX.  P.  207.  1874. 

Schiotz — Mensur.  ophth.  de  I'astig.  Cong,  d'ophth.  de  Milan.  Compt  Rend.  P. 
12.  1881. 

Schiotz — Ophthalmometer  de  Javal  et  Schiotz.  Norsk.  Magaz,  for  Lagevid.  R  3 
Bd.  13.  P.  214.  1882. 

DeWecker  et  Masselon — Un  nouveau  astigmometre.  Gaz.  Med.  de  Paris.  6  S. 
IV.  P.  398.  1882. 

DeWecker  et  Masselon — Astigmometre.  Ann.  d'Oculist.    Juil.  Aout. 

DeWecker  et  Masselon — La  Keratoscopie  clinique.  Ann.  d'Oculist  XC.  P. 
165.  (1883). 


138  BIBLIOGRAPHY. 

DeWecker  et  Masselon,  Modifct  apportee  a  1'astigmometre.  Ann.  d'oculist 
LXXXIX.  Pp.  138-43.  1883. 

DeWecker  et  Masselon — La  Keratoconometrie.  Rev.  clin.  d'Ocul.  No.  i.  P.  5. 
1884. 

Wicherkiewicz,  B — Keratoskopie,  Przeglad  lekarski  (Polish).     No.  7.     1884. 


CHAPTER   X. 


SYMPTOMS  OF  ASTIGMATISM. 

§  161.  From  what  has  gone  before  it  will  be  readily  under- 
stood that  one  of  the  most  prominent,  in  fact  a  characteristic, 
subjective  sign  of  astigmatism  is  diminished  visual  acuteness; 
and  so  it  is  when  we  come  to  examine  these  eyes  in  a  scien- 
tific manner.  But  it  is  not  always  impaired  vision  which 
brings  astigmatics  as  patients  to  the  surgeon.  A  very  consid- 
erable amount  of  bad  vision  often  escapes  the  notice  of  ordi- 
nary patients  suffering  from  astigmatism.  Having  never 
seen  well  at  any  time  in  their  lives  they  have  no  stand- 
ard of  comparison  in  their  own  experience  and  a  careful  edu- 
cation of  the  sense  of  vision  has  made  up  largely  for  indistinct 
retinal  images,  and  so  it  happens  that  they  not  infrequently 
flatter  themselves  that  their  visual  acuteness  is  above  the 
normal.  "  My  eyesight  is  very  good ;  I  can  often  see  things 
other  people  can't,"  is  an  expression  heard  almost  every  day 
in  the  consultation-room,  and  great  is  the  astonishment  of 
these  patients  when  a  rigid  examination  by  the  test-types 
shows  a  reduction  of  vision  to  1/3  or  1/3  of  the  normal. 

§  162.  Persons  with  degrees  of  astigmatism  even  above  the 
medium  may  reach  middle  life  without  being  conscious  of  their 
defect,  and  then  their  attention  is  only  called  to  it  when  their 
presbyopia  drives  them  to  an  examination  for  glasses.  An  in- 
stance of  this  is  the  following  : 

Mrs.  G.,  aged  49,  came  to  my  office  one  day  recently  with  her  daughter  who  was 
under  care  for  an  asthenopia  associated  with  hypermetropia,  and  mentioned  casual- 
ly in  conversation  that  she  had  given  up  reading  in  the  evening  because  she  could 
get  no  glasses  to  suit  her.  She  attributed  this  to  age  and  had  resigned  herself  to  the 
situation.  Upon  my  suggesting  that  probably  some  glasses  might  be  found  which 
would  give  her  good  vision  she  submitted  to  an  examination.  It  was  found  that  in 
either  eye  unaided  by  glasses  V=*/24-  In  the  left  with  -[-0.75  spherical  it  was  some- 
what improved,  but  with  no  other  spherical  glasses  was  it  materially  benefited.  The 

(139) 


I4O  ABSENCE    OF    ASTHENOPIA    IN    SOME   CASES. 

only  line  in  Snellen's  fan  that  she  could  see  without  glasses,  as  a  line,  was  the  hori- 
zontal, and  this  was  also  seen  with  -(-0.75.  Other  -(-  and  —  glasses  made  it  more 
indistinct  It  was  only  when  a +5.25  spherical  was  placed  before  the  eye  that  the 
center  line  came  out  sharply,  and  then  the  other  lines  approaching  the  horizontal 
became  totally  indistinguishable.  With  a  -f  O-7S  O  +4-5cr  axis  9°°  vision  came  up 
to  nearly  4/4  and  the  fan  was  uniform.  An  examination  of  the  R.  E.  made  in  the 
same  manner  showed  an  obliquity  of  the  axis  of  the  meridian  approaching  the  hori- 
zontal of  10°  to  the  outer  side,  and  this  was  confirmed  by  the  keratometer  of  Javal- 
This  instrument  showed,  when  the  arc  was  at  100°,  R=8'/i  mm.;  when  it  was  at  10°, 
R=9  mm.  and  in  the  latter  position  there  was  an  overlapping  of  the  double  images  of 
4l/a  steps  on  the  graded  band.  With  4-0.75  C  +4«5  axis  IOO°>  V=*/s-  The  keratome- 
ter also  confirmed  the  diagnosis  of  the  astigmatism  of  the  L.  £.,  both  as  to  degree 
and  direction  of  the  meridians.  She  had  never  suffered  from  asthenopia  and  during 
her  life  had  done  a  great  deal  of  fine  needle  .work.  A  new  world  was  opened  up  to 
her  by  means  of  her  correcting  glasses,  she  being  then  for  the  first  time  aware  that 
she  did  not  enjoy  ordinarily  good  vision  and  could  hardly  be  convinced  that  most 
people  saw  as  well  without  glasses  as  she  did  with  them.  With  +2*  added  to  her 
correction  for  distance  she  was  able  to  read  the  finest  print  in  the  evening  for  any 
length  of  time. 


§  163.  Cases  as  extreme  as  the  above  are  exceptional,  but 
it  is  not  at  all  uncommon  for  the  lower  forms  of  astigmatism, 
from  0.5  D  to  I  D  to  make  themselves  felt  first  when  the  ac- 
commodation begins  to  fail.  Young  himself  said,  speaking  of 
the  influence  of  his  astigmatism  of  l/u  on  the  acuteness  of 
vision  that  "he  believed  he  could  examine  minute  objects  with 
as  much  accuracy  as  most  of  those  whose  eyes  are  differently 
formed."  Javal  is  of  the  opinion  that  in  childhood  and  youth 
there  is  very  commonly  a  masking  of  the  corneal  astigmatism 
by  means  of  a  partial  accommodation,  believing  that  when 
lenticular  astigmatism  is  present,  it  is,  in  the  majority  of  cases, 
neutralizing  in  its  character.  When  age  begins  to  affect  the 
plasticity  of  the  lens  and  the  activity  of  the  ciliary  muscle, 
this  power  of  unequal  accommodation  is  lost  and  the  latent 
astigmatism  becomes  manifest.  How  far  this  is  true  will  be 
shown  by  a  more  extensive  use  of  the  keratometer,  and  a  com- 
parison of  the  corneal  with  the  total  astigmatism  before  and  after 
paralysis  of  the  accommodation. 

§  164.  But  a  complaint  of  astigmatics  more  common  than 
dimness  of  sight,  though  generally  associated  with  it,  is  asthe- 
nopia,  or  painful  vision.  When  the  eyes  are  used  for  close 


ASTHENOPIA.  14! 

work,  such  as  reading,  writing,  fine  sewing,  etc.,  for  any  con- 
siderable length  of  time,  there  is  pain  accompanied  frequently 
with  a  sudden  indistinctness  of  vision  when  the  effort  is  pro- 
longed. This  asthenopia  may  be  of  all  degrees  of  intensity 
from  a  slight  feeling  of  fatigue  to  a  pain  so  severe  as  to  prac- 
tically make  any  use  of  the  eyes  for  near  work  impossible. 

The  asthenopia  of  astigmatism  is  of  two  kinds,  which  are 
usually  denominated  muscular and  nervous. 

The  first  named  form  has  its  seat  in  the  muscle  of  accom-  JL-- 
modation,  being  sometimes  called  accommodative  asthenopia, 
and  the  fatigue  comes  from  the  irregular  and  spasmodic  con- 
tractions of  the  ciliary  muscle.  The  eye  instinctively  en- 
deavors to  have  as  clear  and  distinct  retinal  images  as  is  pos- 
sible. An  image  distinct  in  all  its  parts  is  impossible  in  astig- 
matism, but  by  a  kind  of  "see-saw"  action  of  the  ciliary  mus- 
cles, first  one  part  of  the  object  and  then  the  other  can  in  the 
majority  of  cases  have  its  image  properly  focussed  on  the 
retina.  So  long  as  it  possible  to  see  more  clearly  and 
satisfactorily  by  this  kind  of  muscular  action  there  is  an  irre- 
sistible temptation  to  use  it ;  and,  as  is  well  known,  nothing  is 
more  wearing  on  the  muscular  energy.  A  regular  systematic 
contraction  of  a  muscle  may  be  continued  for  an  almost  indefi- 
nite time  without  fatigue,  but  convulsive-like  movements  soon 
exhaust  its  power.  When  general  hypermetropia  is  present, 
and  sometimes  when  it  is  not,  this  fatigue  of  the  muscle  is 
often  followed  by  a  suspension  of  its  action  with  consequent 
indistinct  retinal  images. 

In  the  highest  degrees  of  astigmatism  where  no  amount  of 
accommodation  can  give  distinct  retinal  images  of  any  portion 
of  objects  there  is  no  temptation  to  strain  it,  and  as  a  conse- 
q  uence  we  do  not  find  asthenopia  of  this  kind  so  often  a 
symptom  in  the  higher  degrees  as  in  the  lower. 

§  165.  As  is  the  case  in  the  other  forms  of  accommodative 
asthenopia,  the  pain  is  not  usually  referred  to  the  eyes  them- 
selves, but  manifests  itself  under  some  form  of  headache.  The 
pain  may  be  localized  in  any  or  all  of  the  branches  of  the  fifth 
pair  of  nerves,  but  in  a  majority  of  cases  the  headache  is  fron- 


142  NEURALGIA    FROM    EYE-STRAIN. 

tal  with  a  sense  of  constriction  across  the  brow.  It  may,  how- 
ever, be  general,  and  in  some  instances  purely  occipital,  and 
its  connection  with  the  eyes  remain  for  a  long  time  unsus- 
pected. The  irritation  may  be  reflected  to  other  parts  of  the 
body  and  manifest  itself  under  many  curious  forms,  nausea 
being  a  not  uncommon  one. 

The  relation  of  headaches  and  anomalies  of  refraction  as  ef- 
fect and  cause  has  been  long  known  to  ophthalmologists,  but 
the  profession  at  large  in  this  country  were  not  impressed  with 
its  importance  from  the  point  of  view  of  general  medicine  un- 
til Dr.  S.Weir  Mitchell  called  their  attention  to  it  in  1876.  The 
general  practitioner  to  whom  these  patients  first  appeal  for  the 
relief  of  their  persistent  headaches  is  very  liable  to  overlook 
their  real  cause  and  will,  of  course,  fail  to  give  the  desired  relief, 
as  the  following  case  well  shows : 

Mrs.  P.,  aged  40,  had  been  affected  with  severe  headaches  for  many  years  and  suf- 
fered much  at  the  hands  of  many  physicians  for  its  relief.  The  attacks  would  oc- 
casionally come  on  without  any  assignable  cause,  but  would  always  follow  any  at- 
tempt to  use  the  eyes.  Her  indistinctness  of  vision  was  not  such  as  to  call  the  at- 
tention of  her  medical  attendants  to  her  eyes,  and  the  pain  in  them  was  considered 
as  a  part  of  the  "neuralgia."  It  was  impossible  for  her  to  read  for  more  than  ten 
minutes  without  bringing  on  an  attack.  Finally,  owing  to  the  death  of  her  husband, 
it  became  necessary  for  her  to  enter  as  clerk  in  one  of  the  departments  where  she 
would  be  compelled  to  use  her  eyes  for  eight  hours  a  day.  This,  under  the  then  ex- 
isting circumstances,  was  impossible.  In  her  despair  she  applied  to  still  another 
physician  who,  suspecting  that  the  refractive  condition  of  the  eye  might  have  some- 
thing to  do  with  the  trouble,  sent  her  to  me  for  examination.  I  found  a  simple  hy- 
permetropic  astigmatism  of  VH  axis  of  the  correcting  cylinders,  R  45°,  L  135°.  \Vith 
these  V  =  ""/so,  and  she  was  able  to  read  with  them  with  proper  correction  of  pres- 
byopia without  any  considerable  inconvenience  or  pain.  She  obtained  her  place  in 
the  Department  and  went  immediately  to  work,  and  for  more  than  six  years  has  con- 
tinued to  use  her  eyes  at  very  trying  work  from  9  a.  m.  to  4  p.  m.  without  any  ma- 
terial discomfort,  and  her  headaches  have  entirely  ceased.  Occasionally  when  run 
down  by  work  in  the  hot  weather  her  eyes  trouble  her  somewhat,  but  a  few  days  rest 
brings  her  back  to  a  condition  of  ordinary  comfort.  There  is  no  ophthalmic  surgeon 
of  experience  but  can  produce  cases  as  severe  in  their  character  followed  by  relief  as 
speedy  as  this  one  from  the  proper  adaptation  of  glasses. 

§  166.  The  other  form  of  asthenopia  is  nervous.  The  term 
is  a  broad  one,  but  it  must  necessarily  be  so  in  order  to  cover 
the  vagueness  of  our  knowledge  concerning  it.  The  pain  is 


VARIOUS    OTHER    NERVOUS    DISTURBANCES.  143 

» 

not  muscular  in  its  character  and  is  not  always  dependent  upon 
close  application  of  the  eyes  in  near  work.  Moreover,  it  is 
most  commonly  found  in  persons  of  neurasthenic  tendencies. 
The  fatigue  is  a  mental  one  if  we  may  so  express  it.  Indis- 
tinct images  are  abhorent  to  the  visual  consciousness  in  the 
same  manner  as  discordant  sounds  are  abhorrent  to  the  audi- 
tory consciousness,  and  there  is  an  instinctive  tendency  to  get 
away  from  them.  Something  of  this  feeling  may  be  experi- 
enced by  the  emmetrope  on  rendering  himself  artificially  astig- 
matic by  means  of  a  pair  of  cylinders. 

The  manifestations  of  this  asthenopia  are  frequently  feelings 
of  general  discomfort,  associated,  it  may  be,  with  dizziness,  nau- 
sea and  even  vomiting.  But  often  it  is  one  of  actual  pain  re- 
ferred not  uncommonly  to  parts  not  connected  directly  with 
the  eyes.  As  in  other  forms  of  neurasthenic  asthenopia,  there 
may  be  intolerance  of  artificial  or  glaring  light,  and  all  kinds 
of  abnormal  sensations  referable  to  the  eyes  and  their  adnexa. 
Chorea  and  other  nervous  disturbances  of  a  general  nature  are 
laid  at  the  door  of  astigmatism. 

§  167.  These  symptoms  as  well  as  those  of  muscular  asthe- 
nopia sometimes  make  their  appearance  suddenly  after  a  severe 
illness  or  as  the  result  of  some  depressing  causes  operating  to 
lower  the  tone  of  the  nervous  system,  and  may  be  the  first  in- 
timation to  the  patient  of  the  existence  of  an  astigmatism. 
They  continue  in  a  greater  or  less  degree  in  some  cases,  after 
the  refractive  anomaly  has  been  corrected,  necessitating  most 
careful  and  systematic  use  of  the  eyes. 

§  168.  Both  forms  of  painful  vision  as  well  as  the  complaints 
of  diminished  visual  acuteness  are  more  common  when  the 
meridians  are  oblique  than  when  they  are  horizontal  and  verti- 
cal. The  reason  of  this  most  probably  is,  that  when .  the  meri- 
dians lie  near  the  horizontal  and  vertical,  it  is  possible  by  using 
one  or  the  other  focal  plane  to  see  clearly  at  least  a  part  of  the 
letters  whose  strokes  run  usually  in  these  directions ;  when  the 
meridians  are  oblique  the  lines  forming  the  majority  of  the  let- 
ters are  blurred. 

§  169.  Objectively  there  is  little  to  be  seen  different  from  the 


144  SOME   OBJECTIVE   EVIDENCES.  4 

normal.  There  is,  however,  sometimes  found  a  persistent 
frown  associated  with  a  narrowing  of  the  palpebral  aperture. 
This  is  the  result  of  the  habit  the  astigmatic  has  acquired  of 
cutting  off  some  of  the  circles  of  diffusion  by  means  of  the  lids, 
thereby  diminishing  the  indistinctness  of  the  retinal  images. 

§  170.  Persistent  blepharitis  and  chronic  hyperaemia  of  the 
conjunctiva  are  frequent  accompaniments  of  astigmatism  as 
well  as  of  the  other  refractive  anomalies,  and  when  found  on 
examination  of  a  patient  should  always  lead  to  an  investigation 
of  the  optical  condition  of  the  eye.  It  often  happens  that 
these  conditions  when  associated  with  errors  in  refraction  dis- 
appear as  if  by  magic  when  correcting  glasses  are  worn. 

Dr.  Martin  of  Marseilles  ascribes  a  form  of  keratitis  to  astig- 
matism, but  it  seems  to  us  that  sufficient  data  are  not  at  hand 
to  establish  a  positive  connection  between  the  two  as  cause 
and  effect. 

§  171.  It  is  quite  common  for  astigmatics,  even  those  hav- 
ing the  hypermetropic  form,  to  consider  themselves  myopic, 
because  they  have  to  bring  fine  objects  close  to  the  eye  in  or- 
der to  see  them  distinctly.  The  true  explanation  of  this  near- 
sightedness  is  that  on  a  near  approach  of  the  object  the 
increase  in  the  size  of  the  retinal  image  makes  up  to  some  ex- 
tent for  its  indistinctness  of  outline. 

§  172.  Astigmatism  has  also  been  considered  as  an  active 
factor  in  the  production  of  true  myopia,  and  quite  a  num- 
ber of  cases  have  been  cited  in  which  simple  myopic  or  hy- 
permetropic or  comp.  hypermetropic  astigmatism  have  been 
observed  to  pass  over  into  the  myopic  forms.  As  the  same 
can  be  said  of  general  hypermetropia,  it  would  seem  that  as- 
tigmatism could  hardly  be  charged  with  this  per  sc.  It  is  quite 
possible,  however,  that  the  close  approximation  of  the  work 
mentioned  in  the  preceding  paragraph  as  the  result  of  bad 
vision  might  ultimately  lead,  with  an  existing  predisposition 
to  myopia,  to  the  development  of  a  true  axial  myopia,  and  it 
is  also  possible  that  under  these  circumstances  some  of  the  as- 
thenopia  complained  of  is  due  to  the  unusual  strain  on  the 
internal  recti  muscles. 


BIBLIOGRAPHY.  145 

BIBLIOGRAPHY. 


Badal — Etudes  sur  1'etiolog.des  maladies  des  voies  lach.  et  en  partic.  sur  une  cause 
freqnt.  de  ces  malades  meconnue  jusqu  'a  ce  jour.  Ann.  d'oculist.  T.  LXXVIII. 
P.  547. 

Bailey.  W.  A. — Astig.  considered  in  its  relation  to  headache  and  to  certain  morbid 
conditions  of  the  eye.  Guys' Hosp.  Rep.  P.  I.  1878. 

Bull — The  connect,  bet.  chorea  and  errors  of  refrct.  of  the  eye.  N.  Y.  Med.  Rec. 
P.  648.  1878. 

Businelli — Un  cas  d'astig.  Giorn.  d'oftalmol.  Ital.     T.  VII.     P.  10.     1864. 

Cuignet — Un  cas  d'astig.  avec  ses  consequen.  myop.,  keratoscop.,  retinoscop.  et. 
fonctionelles.  Rec.  d'Ophth.  33.11.  Pp.  5204.  Paris.  1880. 

Donders,  F.  C. — Ueber  einen  Spannungsmesser,  (ophthalmotonometer).  Ueber 
Glaucom.  Astig.  u.  Sehscharfe.  Graefes  Arch.  Arch.  B.  IX.  Abt.  II.  P.  215. 
1863. 

Giraud-Teulon,  J.  Geurin,  et  Warlomont,  Polemique.  Astig  et  asthenop  mus- 
culaire.  Ann.  d'oculist.  T.  XLVIII.  P.  296.  1862. 

Giraud-Teulon —  Lettre  sur  quelques  points  relatifs  a  1'asthenop.  et  &  1'astig. 
Gaz.  Med.  de  Paris.  XVII  33.  Pp.  781-4.  1862. 

Green,  J. — On  astig.  as  an  active  cause  of  myopia.  Trans.  Amer.  Ophth.  Soc.  Pp. 
105-8.  1871. 

Green,  J. — On  astig.  considered  in  its  relations  to  defect,  vision,  asthenop.  and 
myopia.  Amer.  Jr.  Med.  Sc.  LIV.  Pp.  82-94.  1867. 

Hall,  L.  B  — A  contrib.  to  the  study  of  blepharitis  ciliaris  from  ametropia.  Med 
Rec.  N.  Y.  XXI.  P.  399.  1882. 

Hewetson,  H.  B. — The  relation  between  sick-headache  and  defective  sight  chiefly 
resulting  from  astigmatism  ;  their  pathology  and  treatment  by  glasses.  Med.  Times 
and  Gaz.  March  1885.  P.  375. 

Hocquard,  E.— Etude  clin.  sur  un  cas  d'asthenop  muscul.  par  astig.  myop.  simpl. 
Rec.  de  mem.  de  med.  milit.  Sept.  and  Oct.  1877. 

Javal,  E.— De  1'astig.  au  point  de  vue  de  1'hygiene.  Rev.  de  hyg.  II.  Pp.  990-9 
Paris.  1880. 

Keyser,  P.  B.— Blepharitis  and  ametropia.  Phila.  Med.  Times.    P.  266.  1877. 

Korner,  V.— Influenzia  de  los  vicios  de  refract,  i  de  la  estroflex.  de  los  puntos 
lacrimales  como  causas  de  conjunct,  cronica.  Rev.  med.  de  Chili.  2  X.  P.  315. 
1881, 

Kugel,  L. — Ueber  Schiefsehen  bei  Astig.  Wien.  med.  Wchnschr.  XIII.  Pp.  420-35- 
52.  1863. 

Kiigel,  L.— Ueber  Sehscharfe  bei  Astig.  Graefes  Arch.  B.  XI.  Abt.  I.  P.  106. 
1865. 

Martin,  G. — Sur  le  rapport  qui  existe  entre  une  variete  de  la  .keratite  'grave  dite 
scrofuleuse  et  1'astig.  de  la  co rnee.  Ann.  d'oculist.  T.  XC.  P.  14.  1883. 

Martin,  G.— A  propos  de  la  keratite  astig.  j,Rev.  gen.  d'ophth.  T.  III.  No.  ,4.  _  P. 
145.  1884. 

Martin,  G.— Deux,  contrib.  a  1'etude  de  la  keratite  astig.  Ann.  d'oculist.  /T.~XC  I. 
P.  44.  1884. 


146  BIBLIOGRAPHY. 

Martin,  G.— Quat  contrib.  a  1'aude  de  la  keratite  astig.    Ann.  d'oculist.  T.  XCII. 

P.  37-    1884. 

Martin  G. — Blepharospasme  astig.    Ann.  d'oculist.    T.  XCI.  P.  231.     1884. 

Masson — Etude  sur  1'astig.  corneen  et  la  percept,  des  couleurs  chez  les  op£res  de 
cataracte.    These  LyOn.    1883. 

Matlie wson.  A. — On  asthenop.  and  the  use  of  glasses.    N.   Y.    Med.   Gaz.     Mch- 
II.    1871. 

Mengin — Note  sur  un  phenomene  subjct  produit  par  un  astig.   myop.   compose. 
Rec.  d'ophth.    3  S.  IV.    Pp.  7-9.    Paris.    1882. 

Mitchell,  S.  W. — Headaches  from  eye-strain.  Am.  Jr.  Med.  Sc.  April.  P.  374. 
1876. 

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Murrell,  J.  E. — Errors  of  refract  of  the  eye.  Richd.  and  Louisville  Med.  Jr.  Sept 
P.  218.  1877. 

Peschel,  M. — Ueber  den  Astig  des  indirect  Sehens.  Arch.  f.  d.  ges.  Physiol. 
XVII.  Pp.  504-10.  Bonn.  1878. 

Prouff,  J.  M. — De  la  sclerotoscopie.  Methode  a  suivre  pour  lesobservaU  ayant  trait 
a  la  keratite  pretendue  astig.  Rev.  clin.  d'Ocul.  No.  2.  P.  25.  1884. 

Reynolds,  D.  S. — Clinic,  observat  on  astig.  Tr.  Am.  Med.  Ass.  XXXII.  P.  231. 
1882. 

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Savage,  G.  C. — Sick-headache,  its  cause — its  cure  etc.  Phila.  Med.  and  Surg.  Jr. 
P.  117.  July  29,  1882. 

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Stevens,  G.  F. — Some  remarks  upon  the  relations  bet  anomal.  refract  of  the  eyes 
and  certain  nervous  diseases.  N.  Y.  Med.  Jr.  P.  561.  Sept  2.  1876. 

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CXL,  Pp.  383-97.  1875. 

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Pp.  310-18.  1875. 

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CHAPTER  XL 


CAUSES  OF  ASTIGMATISM — LENTICULAR  ASTIGMATISM. 

173.  Astigmatism  maybe  congenital  or  acquired.  With  rare 
exceptions  regular  corneal  astigmatism  is  congenital  and  in  quite 
a  considerable  percentage  of  cases  hereditary.  It  is  by  no 
means  uncommon  to  fiftd  several  members  of  the  same  family 
affected  with  astigmatism,  though  it  may  be  of  different  kinds 
and  in  various  degrees. 

§  174.  As  all  eyes  are  more  or  less  astigmatic,  and  abnormal 
differs  from  normal  astigmatism  only  in  degree,  it  is  a  rational 
inference  that  the  manner  in  which  the  eye  is  developed  has 
something  to  do  with  this  peculiar  formation  of  the  cornea. 
Moreover,  we  should  expect  its  shape  to  be  influenced,  to  some 
extent,  by  the  manner  in  which  the  tissues  surrounding  it — 
lids,  orbit,  etc. — are  developed.  Dealing  now  in  what  we  ac- 
knowledge to  be  pure  speculation,  it  seems  probable  that  the 
formative  influences  at  work  on  the  eyeball,  would  result,  if  left 
alone,  in  the  production  of  a  spherical  form  of  the  cornea ;  but 
from  some  cause,  inequality  in  pressure,  unequal  traction  or 
the  like,  the  sphere  is  compressed  and  the  result  is  a  spheroid 
such  as  we  find  it. 

Javal,  among  others,  has  attempted  to  trace  a  connection 
between  the  general  shape  of  the  skull  and  the  shape  of  the 
eyeball  as  expressed  in  its  astigmatism.  In  fact  he  has  for- 
mulated a  law  which  he  thinks  warranted  by  the  facts  in  the 
case,  which  is  :  "  The  meridian  of  greatest  refraction  corres- 
ponds to  the  shortest  diameter  of  the  skull."  This  law  has 
not,  we  believe,  been  fully  verified  by  the  observation  of 
others,  though  there  is  unquestionably  something  of  truth  in 
his  general  proposition.  Further  observations  are  needed  on 
this  point  which  has  also  a  high  ethnographic  interest. 

(147) 


148  ASTIGMATISM    FROM    CORNEAL   WOUNDS. 

»"  §  175.  Regular  astigmatism  may  also  be  acquired.  Any  form 
^  of  traumatism  affecting  the  anterior  portion  of  the  eye-ball  may 
have,  as  a  result  of  its  cicatrization,  an  altered  curve  of  the  cor- 
nea. The  most  common  of  these  traumas  is  the  extraction  of 
cataiact.  That  so  extensive  an  incision  as  that  employed  in 
the  various  forms  of  extraction,  should  leave  behind  it  some 
change  in  the  corneal  curvature  is  not  at  all  astonishing.  It 
can  only  be  exceptionally  that  the  coaptation  of  the  wound 
would  be  so  perfect  as  to  leave  no  trace  on  the  form  of  the  cor- 
neal surface.  These  suppositions  have  been  fully  confirmed  by 
measurements  of  the  cornea  before  and  after  the  operation. 
When  the  cornea  is  measured  within  ten  or  fourteen  days 
after  the  operation,  the  meridian  of  least  curvature  is  found, 
with  rare  exceptions,  to  be  at  right  angles  to  the  direction  of 
the  incision,  and  as  the  section  is  generally  made  upward  or 
downward,  the  less  refracting  meridian  is  the  vertical. 

The  amount  of  astigmatism  at  this  period  is  sometimes  enor- 
mous. In  one  of  my  cases,  where  I  had  reason  to  suppose  a 
tardy  union  of  the  wound,  it  amounted  to  15  D.,  and  Laquer 
reports  one  of  16  D.  minus  refraction.  Such  great  differences 
should  always  lead  us  to  suspect  some  interference  with  prompt 
healing.  When  the  progress  of  the  case  is  normal,the  astigmatism 
commonly  begins  from  the  tenth  day  to  diminish,  and  occa- 
sionally a  complete  cicatrization  may  bring  about  a  shortening 
of  the  radius  in  this  meridian,  rendering  it  the  most  highly  re- 
fracting. In  one  case  under  my  observation,  the  refraction  in 
the  vertical  meridian  passed  over  from  1 1  D.  fourteen  days 
after  the  operation  to  20  D.  eight  weeks  after.  Further  obser- 
vations and  examinations  may  lead  us  to  the  discovery  of  that 
form  of  incision  and  its  position  which  is  less  likely  to  leave  an 
important  permanent  deformity  of  the  corneal  curve.  All 
kinds  of  perforating  wounds  and  ulcerations  of  the  cornea,  par- 
ticularly at  its  margin,  very  frequently  leave  behind  them,  in 
addition  to  the  usual  irregular  astigmatism,  a  greater  or  less 
amount  of  the  regular  form  which  can  often  be  corrected  with 
decided  benefit  to  vision. 

§  176.  Keratoconus,  keratectasia  and  other  similar  alterations 


REGULAR    ASTIGMATISM    IN    KERATOCONUS.  149 

in  the  general  form  of  the  cornea,  while  giving  in  the  majority 
of  cases  a  very  irregular  refraction  may  yet  oftentimes 
have  an  associated  regular  astigmatism  which  can  be  corrected 
with  most  decided  benefit  to  the  patient,  as  the  following  case 
shows: 

Mrs.  JR.,  34  years  old,  saw  well  up'to  her  sixteenth  year.  V  then  began'to  fail  and 
at  her  twenty-first  year  was  st  its  worst.  Since  that  time  it  has  remained  stationary. 
At  the  present  time  V  is  less  than  Veo-  An  examination  showed  the  existence  of 
keratoconus  (in  which  aspect  it  will  be  considered  under  that  heading),  but  meas- 
urements with  JavaPs  keratometer  also  revealed  a  regular  astigmatism.  In  L  at  5° 
to  the  outer  side  of  the  apex,  180°  R=5  mm.  (39.5  D),  90°,  R=6  mm.  (34  D),  with 
a  crossing  of  the  bands  of  6  steps;  in  R,  at  the  same  place,  180°  R=63/*  mm.  (30 
D)  ;  90°  R=5'/2  mm.  (36  D),  with  a  crossing  of  the  bands  to  the  amount  of  61/ 
steps.  With  +4  180°  C  —  3,9o°  in  R,  Vr=*/2« ;  with  —7,  90°  in  L  V=*/«. 

In  the  investigation  of  such  cases  the  ophthalmometer  of 
Javal  is  of  the  highest  value,  and  many  cases  which  have  here- 
tofore been  confined  to  the  stenopaic  slit  or  subjected  to  op- 
eration will  find  a  measure  of  relief  at  least  from  properly 
adapted  cylinders. 

§177.  Lenticidar  Astigmatism.  The  first  case  of  regular 
astigmatism  of  which  we  have  an  accurate  history  was  lentic- 
ular in  its  character.  As  a  matter  of  historic  interest,  I  give 
the  exact  words  in  which  Young  describes  his  condition  as 
found  in  Trans.  Phil.  Soc.  of  Lond.  1801  (not  1793  as  stated  by 
some),  pp.  39-40,  and  contained  in  his  paper  on  the  "  Mechan- 
ism of  the  eye." 

"  My  eye,  in  a  stale  of  relaxation,  collects  rays  which  diverge  vertically  from  an  ob- 
ject at  a  distance  of  10  inches  from  the  cornea,  and  the  rays  which  diverge  horizon- 
tally from  an  object  at  7  inches  distance.  For  if  I  hold  the  plane  of  the  optometer 
(fine  wires)  vertically,  the  images  of  the  line  appear  to  cross  at  10  inches ;  if  horizon- 
tally at  7.  The  difference  is  expressed  by  a  focal  length  of  23  inches.  I  never 
experienced  any  inconvenience  from  this  imperfection,  nor  did  I  ever  discover  it 
until  I  made  these  experiments ;  and  I  believe  I  can  examine  minute  objects  with  as 
much  accuracy  as  most  of  those  whose  eyes  are  cliffei  ently  formed.  On  mentioning 
it  to  Mr.  Gary  he  informed  me  that  he  had  frequently  taken  notice  of  a  similar  cir- 
cumstance, and  that  many  persons  were  obliged  to  hold  concave  glasses  obliquely  in 
order  to  see  with  distinctness,  counterbalancing  by 'the  inclination  of  the  glass  the 
too  great  refractive  power  of  the  eye  in  the  direction  of  that  inclination  (cor.  10. 
Prop.  IV),  and  finding  but  little  assistance  from  spectacles  of  the  same  focal  length. 


I5O  LENTICULAR    ASTIGMATISM. 

The  difference  is  not  in  the  cornea,  for  it  exists  when  the  effect  ol  the  cornea  is  re- 
moved by  a  method  to  be  described  hereafter.  The  cause  is  without  doubt  the 
obliquity  of  the  uvea  and  of  the  crystalline  lens  which  is  nearly  parallel  with  it,  with 
respect  to  the  visual  axis ;  this  obliquity  will  appear  from  the  dimensions  already 
given  to  be  abont  10°.  Without  entering  into  a  very  accurate  calculation  the  differ- 
ence observed  is  found  (by  the  same  corollary)  to  require  an  inclination  of  13°  and  the 
remaining  3°  may  be  easily  added  to  the  greater  obliquity  of  the  posterior  surface  of 
the  crystalline  opposite  the  pupil.  There  would  be  no  difficulty  in  fixing  the  glasses 
of  spectacles  or  the  concave  eye-glass  of  a  telescope  in  such  a  position  as  to  remedy 
the  defect" 


Young,  eliminating  the  refraction  of  his  cornea  Jt>y  immersing 
it  under  water,  demonstrated  that  the  astigmatism  of  his  own 
eyes  was  resident  in  the  lens.  This  was  its  commonly  ac- 
cepted seat  until  the  ophthalmometric  measurements  of  Knapp 
suggested  that  the  cornea  might  also  play  a  part.  As  already 
stated  in  Chapter  III  it  is  now  a  well  demonstrated  fact  that 
the  cornea  is  the  principal  seat  of  the  anomaly.  The  lens, 
however,  not  unfrequently  adds  its  quota  to  the  making  up  of 
the  total  astigmatism  of  the  eye  ;  sometimes  by  increasing  and 
sometimes  by  diminishing  that  of  the  cornea. 

§  178.  The  lens  may  effect  an  astigmatic  action  in  two 
ways;  (a.)  by  a  malposition  and  (£.)by  a  change  in  the  refraction 
of  its  meridians. 

A  dislocation  of  the  lens  in  order  to  produce  an  astigmatic 
effect  must  so  change  its  position  on  the  optical  axis  that  it 
shall  lie  obliquely  to  the  direction  of  the  rays  striking  its  sur- 
face, as  considered  in  §  2$  ;  a  simple  displacement  perpen- 
dicular to  the  optical  axis  will  not  give  rise  to  astigmatism. 
Young,  as  already  stated,  attributed  his  astigmatism  to  such 
an  oblique  position  of  the  lens. 

Regular  astigmatism  has  also  been  found  after  iritis  and 
after  an  operation  for  pterygium.  Also  in  cases  of  pyramidal 
cataract  and  in  membrana  pupillae  perseverans. 

Some  of  the  cases  of  astigmatism  following  blows  on  the  eye 
are  in  all  probability  due  to  such  a  dislocation  of  the  lens. 
The/0rw  of  the  lens  is  so  subject  to  the  action  of  the  ciliary 
muscle  that  it  is  only  in  exceptional  instances  that  we  can 
consider  the  lens  curvature  apart  from  the  influence,  active  or 


FIG.  B.    The  Eye  Ball  Showing  the  Coats  &c.  of  the  Eye. 


'j    FIG.  C.    Longitudinal  Section  of  the  Eye  and  Orbit 
through  the  Dotted  Line  on  FIG.  A. 


35 


order  on  a  separate  piece  of  paper  from  that  used  for  3 


;tuJy  of  the  following  explanations  will  be  of  value  to  the  dealer  in  optical  & 
business  generally  and  are  worth  remembering. 

DUTIES.  It  will  be  noticed  that  we  show  different  qualities  of  the  same  styles  of  fn 
1  good  goods,  all  steel  goods  being  well  tempered,  the  quality  being  of  the  class  of 
,•  a  finer  grade  of  the  sarfle  style,  it  may  be  depended  upon,  that  the  difference  n 
tier  class  of  trade,  will  find  that  it  pays  to  handle  the  finer  grades,  as  the  differ 

JS  NUMBERING.  All  of  our  lenses,  except  those  in  the  cheapest  rubber  and  ste 
i,  and  numbered  in  both  the  inch  and  dioptral  systems,  a  comparative  table  of  w 

PTRAL  SYSTEM.  The  entire  discontinuation  of  the  inch  system  will  be  found  to  gre; 
misleading  system  of  no  value  whatever,  falsely  indicating  the  necessity  of  ca: 
there  is  ever  use  for ;  for  instance,  the  difference  between  a  38  and  52  inch  lens  is 
i  12  and  13  inch  lens.  In  the  dioptral  system,  the  lens  of  i  meter '(39rVfr)i  f° 
i  dioptre;  a  lens  of  half  the  power  (twice  the  focal  length,)  is  called  YT.  d 
tour  times  the  focal  length),  is  #  dioptre  and  numbered  0.25  ;  one-eighth  is  numb 
he  best  way  to  became  acquainted  with  the  dioptral  system,  is  to  totally  ignore  t 

:ES  FOR  PRESCRIPTION  WORK.  Prescription  work  and  all  goods  of  a  special  i 
ne  price  list  for  prescription  work  on  page  408,  instead  of  at  prices  quoted  throi 

FEM  OF  STOCK  NUMBERING.     We  have  adopted  the  system  of  numbering  stock 
it  is  generally  known  and  will  be  more  convenient  to  the  trade  than  a  new  syster 


STEEL  SPECTACLES  FOR  GOLD,  SILVER,  GOLDOIN  ALLOY. 

GOLD  FILLED,  SILVERINE  AND 
the  last  figure  of  the  number  is  ALUMINUM  SPECTACLES 

t  temple  wire.  If  the  next  to  the  last  figure  of  the  number  is 

npin  temple.  o  indicates  Ffat  eye  wire,  flat  temple. 

ind  temple.  i         "        oval  eye  wire,  flat  temple. 

If  round  temple.  2        "          "      •'    round  temple, 

grooved  lenses.  3        "          "       "    half  round  temple, 

ing  temple,  usual  joints.  4  beveled  eye  wire,  flat  temple. 

If  riding  temple.  5  for  grooved  lenses,  riding  temple. 

(irt  end  piece  solid  temple..  6        "         riding  temple,  usual  joint, 

round  eye  wire. 

*  -     


LENTICULAR    ASTIGMATISM.  15  I 

passive,  of  this  muscle.  Alteration  in  density  of  the  lens  sub- 
stance which  would  change  its  refracting  power  are  so  irregu- 
lar in  their  nature  that  we  are  compelled  to  look  upon  lenticu- 
lar regular  astigmatism  as  due,  probably  without  exception, 
to  alteration  in  the  curvature  of  the  lens-surfaces,  brought 
about  by  an  unequal  contraction  of  the  ciliary  muscle.  I 
must  confess  to  an  inability  to  understand  how  some  fibres  of 
this  circular  muscle  can  contract  through  the  same  nervous  im- 
pulse more  strongly  than  others,  and  in  just  such  a  way  as 
shall  give  a  regular  astigmatic  form  to  the  lens  surfaces.  Nev- 
ertheless, from  the  experiments  and  observations  of 
Dobowozki,  Javal,  Laquer  and  others,  the  fact  seems  estab- 
lished, and  we  must  accept  it  whether  we  can  satisfactorily  ex- 
plain it  or  not. 

§  179.  As  in  the  other  form  of  lenticular  astigmatism  so  in 
this,  the  total  astigmatism  of  the  eye  may  be  the  result  of  its 
addition  to  or  subtraction  from  the  corneal  astigmatism. 
Javal,  as  already  stated,  is  of  the  opinion  that  in  the  'major- 
ity of  cases  it  is  neutralizing  in  its  effect,  for  in  the  greater  part 
of  the  cases  examined  by  him  before  and  after  paralysis  of  the 
ciliary  muscle,  the  total  astigmatism  was  greater  after  paraly- 
sis, and  corresponded  more  nearly  to  the  corneal  astigmatism 
as  determined  by  his  keratometer.  He  thinks  also  that  in 
youth  many  cases  of  corneal  astigmatism  are  masked  by  an  un- 
equal action  of  the  ciliary  muscle.  Laquer  in  his  measure- 
ments found  that  in  thirty-four  cases  where  the  total  differed 
from  corneal  astigmatism,  in  nineteen  the  corneal  was  greater, 
and  in  fifteen  it  was  less,  and  the  differences  were,  without  ex- 
ception, in  the  lower  grades.  My  own  experience  with  the 
keratometer,  so  far,  would  seem  to  show  that  where  there  is  a 
difference  the  corneal  is,  as  a  rule,  greater  than  the  total  astig- 
matism (see  table  VI).  Of  course  it  is  to  be  remembered  in 
this  connection,  that  in  those  cases  where  the  total  astigma- 
tism is  the  greater  the  assisting  lenticular  astigmatism  may  be 
due  to  the  oblique  position  of  the  lens,  and  that  a  paralysis  of 
accommodation  is  essentiarto  its  positive  exclusion. 

§  1 80.     A  partial  action  of  the  ciliary  muscle  may  also  be 


152  ASTK.MAilS.M    1-ROM    STK  Ali  ISM  US    OPERATION. 

due  to  a  trauma  which  paralyses  some  of  its  fibres  or  the 
nerve  filaments,  just  as  we  see  an  irregular  dilation  of  the 
pupil  as  a  result  of  the  same  cause. 

§  i8r.  It  has  been  supposed  that  the  operation  for  strabis- 
mus might  exercise  some  influence  on  the  corneal  curvature, 
and  Dr.  Noyes  has  reported  one  case  in  which,  after  three 
strabotomies,  the  meridian  of  maximum  curvature  underwent  a 
rotation  of  25°.  The  existence  of  such  an  action  on  the  part 
of  the  operation  for  strabismus,  has  not,  however,  been  demon- 
strated by  keratometric  measurements,  and  it  is  doubtful 
whether  the  corneal  curvature  is  changed  except,  perhaps,  in 
some  very  rare  instance. 


BIBLIOGRAPHY. 


Amadei,  G. — Sulla  craniologia  delle  anomalie  de  refraz.  dell  'occhio.  Ann.  di 
Ottalm.  XI.  P.  I.  1882. 

Berlin — Ueber  traumatisch  linsen  Astig.  Ber.  ii.  d.  Versamml  d.  Ophth.  Gesellsch. 
P.  174-8.  Heidelberg  1877. 

Bono,  G.  B. — Del  rapporto  tra  la  forma  del  cranio  e  la  refraz.  oculaire.  Gior.  d. 
Soc.  Ital.  III.  P.  133.  Milan  1881. 

Bono — Dell  'astig.  negli  operat.  di  cataratt.  p.  estraz.  Gior.  della  R.  Accad.  di 
Med.  de  Torino  N.  3.  1883. 

Bresgen — Zur  Entwicklg.  v.  Refrcts.  u.  Stellungs-Anomalien  d.  Auges  in  Folge  v. 
Nasenerkrankung.  Deutsch.  Med.  Wochenschr.  No.  9.  1884. 

Emmert,  E. — Auge  u.  Schaedel.    Hirschwald.     Berlin,  1880. 

Francke,  E. — Zur  Lehre  von  der  memb.  pupil,  perseverans.  Grafe  Archiv. 
XXX.  4. 

Gosette — L'asthenop.  sua  patologia  e  cura.    Annal.  de  Ottalm.    XII.    3-4.   1884. 

Hirschberg,  J. — Zur  Prognose  der  Glaucomoperation.  Grafe's  Archiv.  XXIV. 
I.  161-194. 

Jaesche — Ueber  die  Beziehungen  gewisser  Augenubel  zum  Bau  d.  Schaedels- 
Dorpat.  Med.  Ztschr.  V.  P.  163-6.  1873. 

Kneis,  Max — Ueber  Spindle-staar  u.  d.  Accommodation  bei  demselben.  Grafe's 
Archiv.  XXIII.  I.  211. 

Kaiser— Die  Theorie  d.  Astig.     Graefes  Arch.    XL     3.     P.  186.     1865. 

Knapp,  J.  H. — Ueber  die  Erfolge  der  Scheiloperation.  Zehend  Monatsbl.  f. 
Augenheilk.  B  I.  P.  471-484.  1863. 

Landesberg,  M. — Ueber  das  Auftreten  v.  regelmassig.  Astig.  bei  gewis.  Refract  u. 
Accommodationsanomal.  Graefes  Arch.  XXVII.  2,  also  in  Centralbl.  f.  prakt. 
Augenhlk.  P.  362.  I  ec.f  1883. 

Lamlolt — Sur  les  causes  d.  anomal.  de  la  refract.    Gaz.   Hebdon.    No.  39.     1877. 


BIBLIOGRAPHY.  153 

Landolt  —  Relat.  bet.  conform,  of  the  cranium  and  that  of  the  eye.  Brit  Med.  Jr. 
I.  P.  507.  1880. 

Laqueur  —  Ueber  die  Kriimmungsverand.  d.  Hornhaut  nach  Operat.  u.  unter  pathol. 
Verhalt.  Ophth.  Gesell.  Heidelberg.  XV. 

Leroy  —  Theor.  de  1'astig.     Arch,  ophth.     I.     P.  220.     1881. 

Landesburg  M.—  Bericht  ueber  123  Staaroperationen.  Grafes  Archiv.  XXIV. 
59-126 

Leroy  —  Optique  physiolog.     Arch,  d'ophth.    T.  I.     No.  3-4. 

Loring,  E.  G.  —  An  astig.  glass  for  catarct.  patients  with  some  remks,  on  the  sta- 
tistics ofvis.  in  catarct.  operat.  Trans.  Amer.  Ophth.  Soc.  P.  108-18.  1871. 

Martin,  George  —  Etudes   d'ophthalmometrie  clinique.      Ann.  d'Ocull.     Mai-Juin. 


Masson,  A.  —  Etude  sur  Pastigmatisme  corneen  et  la  perception  des  couleurs  chez 
les  operes  de  cataracte.     These  de  Lyon.     1883. 

Noyes,  H.  D.—  Astig.  produced  by  tenot.  of  the  rect.  msls.   Tr.  Amer.  Ophth.  Soc. 
II.     Pt  2.    Pp.  128-31.     N.  Y.     1874. 

Pfalz  —  Ophthalmomet.  Uentersuch.  ii  corneal  Astigmatismus  met  dem  Ophthalmo- 
meter  von  Javal  u.  Shlotz.     Grafes  Archiv.    XXXI.     I.     201-228.     1885. 

Pomeroy—  Case  of  acquired  astig.  Tr.  Amer.  Ophth.  Soc.  1867-8.  IV-V.  P.3O. 
N.  Y.  1869. 

Prouff,  J.  M.  —  Pathogen,  de  1'astig.  reg.  produit  par  lacornee.  J.  Soc.  de  Med.  e* 
Pharm.  de  la  Haute  Vienne.  II.  Pp.  66-8.  Limoges.  1880. 

Prouff  —  Antag.  entre  la  myop.  progres.  et  les  forts  degres  d'  Astig.  conform  a  la 
regie.  Rev.  clin.  d'ocul.  du  S.  O.  IV.  No.  6.  P.  too.  1883. 

v.  Reuss  —  Ueber  Astig.  nach  Staar  Extract.  Klin.  Monatsbl.  f.  Augenhlk.  VII- 
Pp.  473-6.  1869. 

v.  Reuss  —  Untersuch.  ii.  den  Einfluss  des  Lebensalter  auf  die  Kriimmung  d.Horn- 
haut  nebst  einig.  Bemerk.  ii.  die  Dimension,  d.  Lidspalte.  Grafes  Arch.  XXVIII. 
P.  27.  1881. 

v.  Reuss  u.  Woinow  —  Ophth.  Studien  ueber  d.  Astig.  nach  Staarextract.  Wien- 
1869. 

Roeder,  W.  —  Ueber  d.  gemeinschaft.  Ursach.  v.  Glaucom,  Myopic,  Astig.  u.  den 
meisten  Catarct.  Arch.  f.  Augenhlk.  IX.  Pp.  164-83.  Wiesb.  1880. 

Roder,  W.  —  Ueber  Kapseldurchschneidungen  und  dadurch  bedingte  Krummungs- 
anderungen  der  menslichen  Hornhaut.  Grafes  Archiv.  XXIII.  4.  29-56. 

Schelske,  R.  —  Ueber  d.  Verhalt.  d.  intraocul.  Druck.  u.  der  Hornhautkriim.  d  . 
Auges.  Graefes  Arch,  X.  II.  P.  I.  1864. 

Schmidt-  Rimpler  —  Zur  Kennt  einig.  Folgezustande  v.  Contusio  bulbi.  Arch.  f. 
Augenhlk.  XII.  2.  P.  135.  1883. 

Schiotz.  Hj.  —  Ein   Fall  von  hochgradigem   Hornhautastigmatismus  nach  Staarex- 
traction.     Besserung  auf  operativen  Wege.    Archiv.  f.  Augenheilk.     XV.     2.  P.  178. 
Sczelkow  —  Verand.  d.  Hornhautkriim.  mit  zunehm.  Alter.      Centralbl.  f.  d.  Med. 
Wiss.     P.  819.     1880. 

Theobald,  S.—  Notes  of  three  cases  of  progressive  astigmatism.  Trans.  Amer^ 
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Webster,  W.  —  A  case  of  mxd.  astig.  supposed  to  have  been  caused  by  the  sucking 
of  the  eye  by  an  infant.  Med.  Rec.  XVIII.  P.  38.  N.Y.  1880. 

Wecker,  L.  —  Sur  1'astig.  d.  ses  rapports  avec  la  conform,  des   os   du   crane.     Bull. 


154  BIBLIOGRAPHY. 

Soc.  d'anthrop.  de  Paris.  28.  IV.  Pp.  545-9.  1869.  Also  in  Klin.  Monatsbl.  f. 
Augenhlk.  VIII.  P.  161-4.  1870. 

Weiss,  L. — Ueber  den  nach  d.  Weberschen  Hohlschnitt  entsteh.  Cornealastig.  u. 
die  Ursache  d.  nach  Extract,  entsteh.  Astig.  iiberhaupt.  Arch.  f.  Augen  u.  Ohrenhlk. 
VI.  P.  58-84.  1877. 

Woinow,  M. — Falle  wo  nach  Staar-ExtrcL  ein  anderer  Grad.  v.  Astig.  vorhand, 
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i87a 

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1871. 


CHAPTER   XII. 


CORRECTION  OF  ASTIGMATISM. 

§  182.  When  a  differential  diagnosis  of  astigmatism  is  once 
accurately  made,  all  the  optical  data  are  at  hand  for  its  correc- 
tion. We  have  only  to  apply  a  cylindrical  glass,  which  ex- 
presses by  its  refracting  power  the  amount  of  astigmatism, 
with  its  axis  in  the  direction  indicated  in  the  diagnosis,  and  the 
eye  is  rendered  non-astigmatic. 

A  knowledge  of  the  exact  inclination  of  the  axis  of  the  cyl- 
inder is,  therefore,  of  the  utmost  importance  in  writing  orders 
for  glasses,  and  it  is  necessary  that  we  have  some  mode  of 
measuring  its  degree.  It  can  be  done  by  drawing  on  a  sheet 
of  paper  a  series  of  radiating  lines  like  Snellen's  fan  at  inter- 
vals of  5°,  and  laying  the  trial  frame  straight  on  them  with  the 
center  of  the  glass  over  the  center  of  the  radiating  lines  and 
noting  with  which  line  the  axis  marked  on  the  cylinder  corres- 
ponds, taking  care  always  to  read  the  degrees  from  \^&  patient's 
left  to  his  right. 

A  much  more  efficient  and  satisfactory  method,  however,  is 
to  have  the  degrees  marked  on  the  trial-frame  itself.  Several 
trial  frames  of  this  kind  have  been  made,  the  best  of  which,  in 
my  opinion,  is  the  one  manufactured  by  Meyrowitz,  of  New 
York,  and  shown  in  Fig.  42.  The  frame  is  constructed  to  hold 
two  lenses  on  each  side,  and  one  of  them  can  be  turned  by 
means  of  the  two  little  knobs  shown  in  the  drawing.  When  in 
an  examination  the  position  of  the  cylinder  where  vision  is  best 
is  found,  the  axis  of  the  cylinder  marked  on  the  glass  points 
to  the  exact  degree  of  inclination.  This  frame  is  further  use- 
ful for  determining  the  distance  between  the  pupils  and  the 

(155) 


56 


DESCRIPTION    OF    AIRY  S    CASE. 


height  of  the  nose,  two  important  factors  in  the   proper  fitting 
of  spectacles. 

Fig.  42. 


MEYROWITZ'S  TRIAL-FRAME.' 


\  183.  The  first  full  account  given  of  the  correction  of  astigmatism  by  cylinders  is 
that  by  the  Royal  Astronomer  Airy,  in  1827.  For  this  reason  and  also  to  show  that 
the  correction  was  based  on  a  scientific  study  of  the  optical  condition,  and  to  give 
the  history  of  the  term  astigmatism  as  applied  to  this  condition,  I  subjoin  an  account 
of  this  case  taken  from  the  last  English  edition  of  Mackenzie's  classical  treatise  on 
the  eye  (London,  1854,  p.  926). 

"  Mr.  Airy  discovered  that  in  reading  he  did  not  usually  employ  his  left  eye,  and 
that  in  looking  at  any  near  object  it  was  totally  useless,  in  fact  the  image  formed  in 
that  eye  was  not  perceived  unless  attention  was  particularly  directed  to  it.  Suppos- 
ing this  to  be  due  entirely  to  habit,  and  that  it  might  be  corrected  by  using  the  left 
eye  as  much  as  possible,  he  endeavored  to  read  with  the  right  eye  closed  or  shaded  j 
but  found  that  he  could  not  distinguish  a  letter,  at  least  in  small  print,  at  whatsoever 
distance  from  the  eye  the  characters  were  placed.  Sometime  afterwards  he  observed 
that  the  image  formed  by  a  bright  point,  such  as  a  distant  lamp  or  star,  in  his  left 
eye,  was  not  circular  as  it  is  in  the  eye  which  has  no  other  defect  than  that  of  being 
near-sighted,  but  elliptical,  the  major  axis  making  an  angle  of  about  35°  with  the 
vertical  and  its  higher  extremity  being  inclined  to  the  right.  Upon  putting  on  con- 
cave spectacles,  by  the  assistance  of  which  he  saw  distant  objects  distinctly  with  his 
right  eye,  he  found  that  to  his  left  eye  a  distant  lucid  point  had  the  appearance  of  a 
well-defined  line,  corresponding  exactly  in  direction  and  nearly  equal  in  length  to 
the  major  axis  of  the  ellipse  above  mentioned.  He  found  also  that  if  he  drew 
upon  paper  two  black  lines  crossing  each  other  at  right  angles  and  placed  the  paper 
in  a  proper  position  and  at  a  certain  distance  from  the  eye,  one  line  was  seen  per- 
fectly distinct  while  the  other  was  barely  visible ;  while  upon  bringing  the  paper 

'The  price  of  this  trial-frame  is  $15.00. 


AIRYS    CASE.  157 

nearer  to  the  eye  the  line  which  was  distinct  disappeared  and  the  other  was  seen 
well  defined.  All  these  appearances  indicated  that  the  refraction  of  the  eye  was 
greater  in  the  plane  nearly  vertical  than  in  that  at  right  angles  to  it ;  and  that,  conse- 
quently it  would  not  be  possible  to  see  distinctly  by  the  aid  of  lenses  with  spherical 
surfaces.  Mr.  A.  found,  indeed,  that  by  turning  a  concave  lens  obliquely,  or  on 
looking  through  a  part  near  the  edge,  he  could  see  objects  without  confusion ;  but  in 
both  cases  the  distortion  was  such  that  he  could  not  hope  to  make  any  use  of  the  eye 
without  some  more  effectual  assistance. 

Mr.  Airy's  object  was  now  to  form  a  lens  which  should  refract  more  powerfully  the 
rays  in  one  certain  plane  than  those  in  the  plane  at  right  angles  to  it ;  and  his  first 
idea  was  to  employ  one  whose  surfaces  should  be  cylindrical  and  concave,  the  axes  of 
the  cylinders  crossing  each  other  at  right  angles  and  their  radii  different.  To  show 
that  this  construction  would  effect  the  purpose,  it  is  only  necessaiy  to  imagine  such  a 
lens  divided  into  two  lenses  by  a  plane  perpendicular  to  its  axis  ;  thus  it  is  easily 
seen  that  the  refraction  of  the  one  will  not  be  perceptibly  altered  by  that  of  the  other 
and  the  whole  refraction  will  be  a  combination  of  the  two  separate  refractions.  The 
rays  in  one  plane  will  be  made  to  diverge  entirely  by  the  refraction  of  one  lens,  and 
those  in  the  other  plane  by  that  of  the  other  lens.  This  construction  was  then  suffi- 
cient ;  but  for  the  facility  of  grinding  and  for  the  diminution  of  the  curvatures,  it 
appeared  preferable  to  make  one  surface  cylindrical  and  the  other  spherical,  both 
concave. 

To  discover  the  necessary  data  for  the  formation  of  the  lens,  Mr.  A.  made  a  very 
fine  hole  with  the  point  of  a  needle  in  a  blackened  card,  which  he  caused  to  slide  on 
a  graduated  scale ;  then  strongly  illuminating  a  sheet  of  paper,  and  holding  the  card 
between  it  and  the  eye,  he  had  a  lucid  point  upon  which  he  could  make  observations 
with  ease  and  exactness.  Resting  the  end  of  the  scale  upon  the  cheek-bone,  and 
sliding  the  card  on  this  scale  he  found  that  what  was  seen  as  a  point  when  close  to 
the  eye,  at  a  distance  of  six  inches  appeared  a  well-defined  line  inclined  to  the  verti- 
cal about  35°  and  subtended  an  angle  of  (by  estimation)  2°;  at  the  distance  of  3l/2 
inches  it  appeared  a  well-defined  line  at  right  angles  to  the  former  and  of  the,  same 
apparent  length.  It  was  necessary,  therefore,  to  make  a  lens  which,  when  parallel 
rays  were  incident  should  cause  those  in  one  plane  to  diverge  from  the  distance  3x/2 
inches,  and  those  in  the  other  plane  from  the  distance  six  inches. 

Having  procured  a  sphero-cylindrical  lens1  of  which  the  radius  of  the  spherical 
measured  3^2  inches  and  that  of  the  cylindrical  surface  4!/2  inches,  Mr.  A.  found 
that  he  could  read  the  smallest  print  at  a  considerable  distance  with  the  left  eye  as 
well  as  with  the  right.  He  found  that  vision  was  most  distinct  when  the  cylindrical 
lens  was  turned  from  the  eyes ;  and  as  when  distant  from  the  eye  the  lens  altered 
the  apparent  figure  of  objects  by  refracting  differently  the  rays  in  the  different  planes* 
he  had  the  frame  of  his  spectacles  made  so  as  to  bring  the  glass  pretty  close  to  the 
eye.  With  these  precautions  he  found  that  the  eye  which  he  had  once  feared  would 
become  quite  useless,  could  be  used  in  almost  every  respect  as  well  as  the  other." 
***** 

"Having  occasion  20  years  after  the  first  account  of  the  malformation  of  his  left 
eye  was  submitted  to  the  Cambridge  Philosophical  Society  (1849)  to  explain  that  a 
change  had  happened  in  the  state  of  the  eye,  Mr.  Airy  took  an  opportunity  of  men- 

1  This  glass  was  made  by  Fuller,  of  Ipswich. 


158  ORIGIN    OF   THE   WORD    ASTIGMATISM. 

tioning  that  as  the  nature  of  the  effect  of  that  malformation  was,  that  the  rays  of  light 
coming  from  a  luminous  point  and  falling  on  the  whole  surface  of  the  pupil  did  not 
converge  to  a  point  at  any  position  within  the  eye,  but  converged  in  such  a  manner 
as  to  pass  through  two  lines  at  right  angles,  the  Rev.  Dr.  Whewell  had  affixed  to  this 
phenomenon  the  term  Astigmatism" 

All  knowledge  acquired  since  this  account  was  published  has  added  nothing 
to  the  theory  of  the  astigmatic  condition  or  to  the  philosophy  of  its  correction. 

Astigmatism,  however,  had  been  corrected  independently,  it  would  seem,  by  a 
number  of  individuals  during  the  years  between  Young's  discovery  of  the  condition 
and  the  beginning  of  the  new  era  inaugurated  by  the  investigations  of  Knapp  and 
Bonders.  The  optician  Gary  informed  Young  that  he  had  found  many  myopes  who 
saw  better  when  their  concave  glasses  were  tilted.  It  also  appears  that  the  painter 
Cassus  noticed  some  peculiarities  in  the  work  of  his  master,  Gros,  at  Paris,  in  1818, 
which  he  referred  to  a  defect  in  sight,  and  that  this  defect  was  corrected  by  cylinders 
made  by  Guscipi,  of  Rome,  in  1840-44,  and  these  were  afterwards  duplicated  by 
Soliel,  of  Paris. 

In  1852  Goulier  sent  to  the  French  Academy  of  Science  a  sealed  communication 
with  the  request  that  it  be  not  opened  until  1865.  When  it  was  examined  it  contained 
a  good  account  of  astigmatism  (given  in  Abstract  in  Javal's  article  on  the  history  and 
bibliography  of  astigmatism  in  Am.  J'Ocu/.,  1866)  and  manner  of  its  correction  by 
cylinders.  A  Swiss  priest,  Snyder,  of  Luzerne,  also  detected  in  himself  an  astigma- 
tism which  he  corrected  by  cylindrical  glasses  in  about  1849. 

Dr.  Isaac  Hays  in  his  American  edition  of  Laurence  on  the  Eye  (1854),  relates  in 
full  a  case  which  had  been  successfully  fitted  with  cylinders  by  the  Philadelphia  op- 
tician. McAllister,  in  1825,  and  two  others  which  had  in  that  year  (1853)  come  under 
his  own  observation  in  which  the  same  optician  had  improved  vision  by  the  same 
means ;  but  no  accurate  account  of  these  last  was  given. 

§  184.  Easy,  however,  as  it  may  appear  theoretically  to  cor- 
rect astigmatism,  when  we  come  to  deal  with  the  question 
practically  it  is  not  always  so  simple  as  it  seems.  We  are 
dealing  here  in  part  with  positive  science  and  it  is  essential  that 
our  methods  should  be  exact  if  we  expect  our  results  to  be 
perfect. 

§  185.  In  the  first  place,  it  is  necessary  that  the  diagnosis  be 
in  all  respects  correct.  We  must  not  only  know  the  inclina- 
tion of  the  faulty  meridian  to  within  5°  (or  even  less  in  some 
cases)  but  the  exact  state  of  the  refraction  in  each  meridian 
separately.  To  obtain  these  in  the  majority  of  cases,  as  we 
have  already  seen,  requires  the  expenditure  of  much  time  and 
patience,  and  the  practitioner  who  hopes  for  uniform  success 
and  satisfaction  in  his  astigmatic  cases  must  grudge  neither. 
In  many  cases  it  is  only  by  examining  and  reexamining  and 


METHOD    OF    RECORDING    CASES. 


159 


testing  and  proving  by  many  methods  that  the  true  condition 
is  revealed,  and  sometimes  it  is  necessary  to  give  glasses  to 
be  worn  for  a  time,  in  order  that  the  close  observation  of  the 
patient  may  throw  some  light  upon  an  obscure  point. 

§  1  86.  The  methods  of  dealing  with  astigmatism  after  a  cor- 
rect diagnosis  has  been  established  may  be  best  shown  by 
some  cases  illustrative  of  the  various  forms  to  be  dealt  with. 

CASE  I.  It  has  been  shown  by  the  various  tests  that  there  is  simple  myopic  astig- 
matism in  the  vertical  meridian.  With  —  2  axis  180°  V=4/4  and  Snellen's  fan  is  uni- 
form and  clear.  You  order: 

L.  R. 

—  2  axis  1  80°.  —  2  axis  1  80°. 

And  if  he  is  a  young  man  of  18  and  a  student,  or  employed  where  he  uses  his  eyes 
constantly  for  close  work,  you  order  him  spectacles  which  he  is  to  use  constantly.  If 
he  thus  early  makes  them  a  part  of  his  eyes  he  places  himself  in  the  condition  of  an 
emmetrope  and  runs  much  less  risk  of  trouble  in  future. 


43- 


DIAGRAM  FOR  RECORDING  ASTIGMATISM  AND  FOR  ORDERING  GLASSES,  REPRESENT- 
ING THE  PATIENT'S  EYES  AS  SEEN  FROM  THE  FRONT. 

We  should  always  in  recording  diagnoses  and  ordering 
glasses  follow  a  uniform  system  in  order  to  avoid  a  trouble- 
some confusion  and  liability  to  error  which  would  otherwise 
inevitably  occur.  We  must  always  consider  the  glasses  as  the 
patient  looks  through  them,  and  in  counting  the  degrees  of  in- 
clination of  the  axis  of  the  cylinders,  proceed  always  from  his 
left  to  his  right ;  and  it  is  well  to  have  this  diagrammatically 
represented  as  in  Fig.  43.  Such  diagrams  are  also  useful  for 


l6o  CLINICAL   CASES. 

recording  graphically  many  other  morbid  conditions  and  in- 
juries of  the  anterior  portion  of  the  eye-ball  and  of  the  lids. 
The  method  of  using  this  diagram  is  shown  in  Figs.  20  and  21. 

CASE  II.  A  lady  of  30  is  found  to  have  compound  hypermetropic  astigmatism 
with  V=*/u.  She  is  unable  to  read  the  evening  paper  with  comfort  and  her  fine 
needle-work  tires  her  eyes  even  in  the  daytime.  There  is  a  general  H  of  1.5  with  H. 
astig.  of  0.75  axis  at  45°  in  L  and  at  135°  in  R.  With  this  correction  V=4/«  and  No. 
I  is  read  with  ease  and  comfort  at  ten  inches.  She  is  ordered : 
L.  R. 

+  1-5  C  + 0.75  45°-          +  1-5  C  +  0.75  135°. 

You  insist  upon  the  importance  of  her  wearing  these  glasses  constantly  in  order  to 
save  her  from  a  possible  future  break-down  ;  but  she  objects  so  strongly  that  you 
feel  perfectly  certain  she  will  not  do  it,  particularly  as  she  says  her  distant  vision  is 
as  good  as  she  cares  about  She  also  rebels  at  spectacles  and  wants  to  know  why 
nose-glasses  won't  do  as  well. 

This  is  the  battle  that  goes  on  in  the  consultation  room  daily,  and  the  surgeon  will 
commonly  find  it  wise  to  effect  some  sort  of  compromise,  particularly  at  the  begin- 
ning. It  is  much  more  satisfactory  and  much  less  trouble  to  the  patient  to  have  cyl- 
inders set  in  spectacle  frames  since  the  axes  are  there  always  at  the  same  angle  and 
require  no  adjustment ;  but  young  women  are,  as  a  rule,  so  opposed  to  wearing 
them,  particularly  in  public,  that  they  will  often  suffer  rather  than  use  them.  They 
find  nose-glasses  less  objectionable,  and  most  opticians  can  now  fit  cylinders  in  them 
so  that  they  can  be  adjusted  properly  on  the  nose  with  little  trouble  after  patients 
have  become  accustomed  to  their  use.  You  therefore  have  one  pair  of  glasses  set  in 
spectacle  frames  for  use  at  home  when  she  is  doing  continuous  work  or  reading,  and 
another  pair  in  pince-nez  for  reading  the  hymns  in  church,  the  programmes  at  con- 
certs or  the  theatre,  for  picture  galleries,  shopping,  etc.  In  the  course  of  time  she 
will  find  her  distant  vision  so  much  improved  by  the  nose-glasses  that  she  will  wear 
them  pretty  constantly,  and  finding  in  the  end  that  the  spectacles  are  much  less 
troublesome  will  most  probably  come  to  substitute  them  for  the  nose-glasses  for  all 
purposes. 

§  187.  Another  condition  which  comes  in  as  a  complication 
is  that  of  presbyopia.  When  the  accommodation  begins  to  fail 
its  effect  must  be  taken  into  consideration,  since  the  same 
glasses  will  no  longer  do  for  far  and  near  vision. 

CASE  III.  A  gentleman  of  48  complains  of  his  inability  to  read  with  comfort  in  the 
evening.  His  distant  vision  has  been  sufficiently  good  for  him  as  a  professional 
man,  though  he  has  always  considered  himself  somewhat  "  near-sighted."  On  test- 
ing it  is  found  that  there  is  myopic  astigmatism  of  V«  in  the  vertical  meridian,  and 
correction  brings  V  up  from  MJy>  to  ^/M.  With  —  '/««  &x^s  l^°°  f°r  DOtn  eyes,  he 
is  not  able  to  read  No.  i  at  12  inches,  but  with  a  +7*8*  placed  in  front  of  the  cylin- 
ders he  reads  it  with  facility  at  from  10  to  1 8  inches.  Instead  however,  of  ordering 


CLINICAL    CASES.  l6l 

him  a  compound  lens  with  a  — V^s0  on  one  face  and  a  -\-l/&B  on  the  other  we  sim- 
ply write  for 

L.  R. 

+1/48.90°  +V«.90°, 

thus  giving  the  optical  result  of  the  combination  ,  for  the  spherical .  -f1/^  neutralizes 
the  — J/48  cylindrical  axis  at  180°  leaving  a  +V*8  action  at  90°,  thus  practically  ren- 
dering the  eye  myopic  Vis  in  all  its  meridians.  This  relieves  the  accommodation 
sufficiently  for  a  time  and  gives  satisfaction. 

CASE  IV.  A  lady,  50  years  of  age,  has  had  great  difficulty  in  getting  glasses  for 
reading.  She  has  gone  from  one  optician  to  another  and  has  accumulated  a  store 
of  glasses  of  various  kinds,  but  they  are  all  unsatisfactory,  and  she  has  at  last  settled 
down  to  the  belief  that  there  are  no  glasses  that  will  fit  her  eyes,  particularly  as  she 
considers  them  "weak,"  her  distant  vision  never  having  been  good.  She  has  at 
last,  however,  been  pursuaded  to  have  her  eyes  examined  by  an  oculist  and  you  find 
after  a  careful  investigation  that  there  is  compound  hypermetropic  astigmatism.  In 
L  -MCH-J-S  axis  7°°  gives  V=4/6;  in  R  +2CH-O.75  axis  60°  gives  V— 4/5,  and  no 
other  glasses  or  combinations  do  better. 

With  both  eyes  corrected  V=4/4  nearly,  and  with  them  the  fan  is  clear  and  uni- 
form. Javal's  keratometer  verifies  the  degree  of  astigmatism  and  the  direction  of 
the  principal  meridians. 

This  case  offers  departures  from  the  usual  in  that  the  general  ametropia  is  different 
in  the  two  eyes  (anisometropia),  while  the  degree  of  astigmatism  is  not  the  same  for 
each  eye,  and  the  direction  of  the  faulty  meridians  is  not  symmetrical.  When  the 
meridians  are  oblique,  as  a  rule,  they  stand  at  the  same  angle  outward  or  inward  for 
each  eye — very  seldom  is  one  outward  and  the  other  inward,  a  fact  which  would 
seem  to  point  to  a  common  formative  cause  at  work  for  the  production  of  the  mal- 
formation. 

With  these  glasses,  however,  she  cannot  read  ;  her  presbyopia  has  to  be  corrected. 
It  is  found  that  by  adding  +2.5S  to  the  distance  glasses  she  can  read  the  finest  print 
with  ease.  You  therefore  order  correction  for  distance,  and  give  her  the  following 
for  reading : 

L.  R. 

+3-5  C +I-5oy  axis  7°°-  +4-5  C  +°-75cy  axis  60°. 

With  her  glasses  life  assumes  a  new  and  decidedly  more  cheerful  aspect.  She 
can  see  at  a  distance  as  she  never  could  before,  and  the  long  hours  of  the  evening 
are  passed  pleasantly  in  reading,  something  that  before  was  impossible. 

CASE  V.  This  is  a  young  man  of  21.  His  vision  is  very  bad,  being  only  4/eo> 
and  a  long  and  careiul  examination  with  sphericals  and  cylindrical  fails  to  bring  it 
up  to  more  than  4/i2  and  he  is  benefited  by  both  -+-  and —  lenses.  The  keratometer 
of  Javal  showed  an  astigmatism  of  4.5  D  at  180°  in  L,  and  the  same  at  25°  in  R.  In 
the  trial  by  lenses,  however,  the  answers  and  statements  are  so  contradictory  and  un- 
certain that  it  is  considered  expedient  to  paralyze  the  ciliary  muscle  in  order  to  get 
rid  of  the  interference  of  the  accommodation.  So  a  drop  of  a  4  gr.  solution  of 
atropia  sulph.  is  ordered  to  be  put  into  each  eye  four  times  a  day  for  three  days  when 
he  is  to  return  for  another  investigation.  His  eyes  are  examined  now  by  the  oph- 
thalmoscope, and  in  the  left  eye  the  fine  vessels  running  horizontally  over  the  sides  of 
the  disk  are  seen  in  the  erect  image  only  when  — 2.75  is  brought  behind  the  hole  in  the 


l62  CLINICAL    CASES. 

mirror.  Through  this  lens  all  the  other  vessels  are  dimmed  in  outline  and  the  finer 
vertical  vessels  near  the  macula  are  not  distinguished  at  all.  These  last  are  seen 
only  when  a  -(-2  is  behind  the  mirror.  This  gives  at  once  a  clue  to  the  condition. 
On  trying  by  the  inverted  method  the  disk  contracts  in  its  horizontal  diameter  and 
enlarges  in  its  vertical  diameter  as  the  lens  is  removed  from  the  eye,  and  the  vertical 
diameter  contracts  and  the  horizontal  enlarges  as  it  is  brought  closer  to  the  eye,  and 
the  ovals  are  vertical  and  hoiizontal.  There  can  be  no  opinion  now  but  that  the 
case  is  one  of  mixed  astigmatism,  and  proceeding,  on  the  indications  thus  furnished, 
to  a  reexamination  with  glasses  we  soon  find  that  with — 2.75°  axis  1 80°,  combined 
with  -}-2c  axis  90°  V=4/5-  In  the  R  eye  the  examination  with  the  direct  ophthal- 
moscopic  method  is  not  so  satisfactory,  but  the  disk  appears  an  oval  standing 
obliquely,  and  when  a  —  3.5  or  — 4.5  is  used  behind  the  mirror,  those 
parts  of  the  vessels  running  obliquely  upward  and  inward  are  most  distinct ;  and 
when  -}-i  or  +1.5  is  used  those  parts  of  the  vessels  running  upward  and  slightly  out- 
ward are  sharpest  in  outline.  In  the  inverted  image  the  disk,  instead  of  being  a  ver- 
tical oval  when  the  lens  is  removed  from  the  eye,  is  oblique  with  its  top  inclining 
outward.  Turning  now  to  the  directions  of  the  corneal  meridians,  as  given  by  the 
keratometer,  we  find  that  the  meridian  of  greatest  refraction  has  its  axis  at  25°, 
and  the  meridian  of  least  refraction  its  axis  at  115°.  A  very  few  trials  with  glasses 
now  show  us  that  with  — 3.5°  axis  25°^  +  1.5°  axis  115°  V=*/«. 


In  ordering  glasses  for  mixed  astigmatism  two  plans  can  be 
followed.  One  is  to  have  one  surface  of  the  lens  ground  as  a 
cylinder,  giving  correction  to  one  meridian,  and  the  other  as  a 
cylinder  correcting  the  other  meridian,  with  their  axes  at 
angles — crossed  cylinders  as  they  are  called.  For  the  above 
case,  therefore,  we  write  : 

L.  R. 

—2.75  180°  C  +2,  90°.  —3.5,  25°  C+i-5,  150°. 

This  is  the  form  of  astigmatic  lens  which,  as  we  have  seen, 
Airy  first  conceived  for  his  own  eye,  and  it  is  considered  by 
many  to  be  the  best  in  some-  particulars.  Among  other  ad- 
vantages it  is  thought  to  give  a  flatter  field.  But  it  is  an  ex- 
pensive lens  to  manufacture  for  the  trade,  and  there  is  more  risk 
of  an  error  in  the  direction  of  the  axis  than  in  the  other  form. 
The  other  plan  is  to  convert  it  into  a  sphero-cylindrical  lens, 
in  which  there  is  only  one  cylinder  to  be  made.  This  is  done 
in  the  following  manner  : 

If  we  take,  for  the  left  eye  in  above  case,  a  — 2.75  piano-spheri- 
cal and  grind  on  the  other  side  a  +4.75  cylinder  we  have  practic- 
ally the  formula  given  above,  for  the  +4.75  cylinder  overcomes 


DIFFICULTY    IN    WEARING    CORRECTING    GLASSES.  163 

the  — 2.75  in  the  meridian  corresponding  to  its  curvature  and 
gives  in  addition  a  -(-  cylindrical  action  of  (4.75-2.75)  2  D,while 
the  —  action  of  2.75  of  the  sperical  lens  in  the  meridian  at  right 
angles  to  it  is  unaffected.  Applying  the  same  principle  to  the 
construction  of  the  lens  for  the  right  eye,  we  would  order : 
L.  R. 

—2-75'  G  +4-75c'v  9°°-  —3-5"  C  +5cy  US0- 

This  method  can  be  'modified  in  many  ways  and  often  to 
the  advantage  of  the  patient's  pocket.  Suppose,  for  example, 
that  both  eyes  of  the  patient  were  affected  with  the  mixed  astig- 
matism of  the  left  eye  of  the  case  just  considered.  When  he 
arrived  at  50  or  53  years  his  reading  glasses  could  be  made  in 
the  form  of  simple  cylinders  +4.75,  9O°,thus  rendering  the  whole 
eye  myopic  2.75  D,  and  relieving  his  accommodation  to  the  de- 
sired extent.  Plane  cylinders  are  not  so  expensive  as  sphero- 
cylinders,  and  we  should  not  be  above  considerations  of  this 
kind,  particularly  for  persons  of  limited  means  who  lose  or 
break  their  glasses  frequently. 

§  1 88.  It  is  a  fact,  however,  which  occurs  with  an  unfortu- 
nate frequency  in  our  clinical  experience,  that  the  glasses  which 
give  perfect  optical  correction,  particularly  if  this  is  deter- 
termined  under  atropine,  cannot  be  worn  with  comfort  and 
sometimes  not  at  all.  Such  cases  are  to  be  found,  as  a  rule, 
in  persons  who  .have  passed  their  youth  with  their  anomaly 
uncorrected.  Of  this  condition  the  following  case  is  an  illus- 
tration. 

CASE  VI.  Mrs.  P.,  set.  30,  has  suffered  from  asthenopia  and  bad  vision  for  a  long 
time,  for  neither  of  which  has  she  found  any  glasses  beneficial.  On  examination  I 
found  V=4/is  in  L,  4/24  in  R.  Plus  glasses  gave  no  improvement,  but  minus  spher- 
ical glasses  from  I  to  3  did  increase  the  visual  acuteness  somewhat  With  — 2.25 
axis  180°  V=4/6  in  L,  lfg  in  R.  An  opthalmoscopic  examination  by  the  direct 
method  showed  no  myopia  in  the  vertical  meridian,  but  on  the  contrary,  a  hyperme- 
tropia  in  the  horizontal  meridian.  This  discrepancy  in  the  findings  by  the  subjective 
and  objective  methods  being  to  me  always  an  indication  for  the  paralysis  of  accom- 
modation, I  ordered  her  to  apply  a  4  gr.  solution  of  atropine  three  times  a  day  and  re- 
port for  reexamination  at  the  end  of  three  days.  Under  the  mydriatic  it  was  found 
that  V=4/eo  in  R,  */36  in  L,  and  with  +2.5°  axis  90,  V=4/9  in  R  and  */e  L.  This 
condition  was  confirmed  by  the  ophthalmoscope.  As  is  my  custom  I  allowed  the 
effect  of  the  mydriatic  to  pass  off  before  ordering  glasses.  At  the  end  of  ten  days 
when  the  pupil  had  regained  its  normal  size,  I  found  that  the  +  cylinders  gave 


164  DIFFICULTY    IN    WEARING    CORRECTING    GLASSES. 

her  no  improvement  for  distant  vision,  but  on  the  contrary,  the  concave  cylinders 
did.  She  was  given,  however,  +2.5°  90°  for  each  eye,  with  instructions  to  gradually 
accustom  herself  to  their  use.  These  instructions  she  followed  faithfully  for  three 
months,  but  at  the  end  of  that  time  loi  nd  herself  in  no  better  condition  than  before. 
Her  vision  for  distance  had  not  improved,  and  while  she  could  see  better  for  close 
work  with  them,  her  asthlnopia  was  not  relieved  ;  in  fact,  the  discomfort  was  greater 
with  the  glasses  than  without  them.  She  could  see  well  with  — 2.y  180°,  and  she 
was  now  ordered  these  for  experiment.  Distant  V  was  more  satisfactory,  but  she 
could  not  use  them  for  near  work.  She  was  in  despair,  when  happening  one  day 
to  pick  up  her  husband's  glasses  that  I  had  prescribed  sometim^  before  for  a  H  of 
0.75  in  the  horizontal  meridian,  she  found  comparative  comfort  in  reading,  and  these 
are  the  only  glasses  that  we  have  found  up  to  this  time  which  are  of  any  material  ad- 
vantage. We  hope,  however,  in  course  of  time  to  be  able  to  educate  her  up  to  the 
use  of  full  correcting  glasses,  by  gradually  increasing  their  power. 

The  case  was  first  examined  before  I  had  any  means  of  keratometric  measurement,but 
lately  I  examined  her  with  Javal's  instrument,  and  found  in  both  ^=8'/i  mm.  at  180° 
and  8'/4  at  90°,  with  a  crossing  of  the  bands  of  a'/z  steps  at  180°,  thus  verifying  the 
diagnosis  made  by  the  other  methods. 

Cases  so  extreme  as  this  are  not  common,  but  lesser  degrees 
are  frequently  met  with.  I  can  only  account  for  them  on  the 
supposition  that  the  eyes  have  been  accustomed  for  so  long  to 
the  astigmatic  state  as  to  make  the  abnormal,  in  a  certain 
sense,the  normal  condition  and  that  the  cerebral  center  for  vision 
resents  an  interference  with  the  established  order  of  things.  It 
must  be  remembered,  in  this  connection,  that  in  dealing  with 
the  human  eye  we  have  to  do  not  with  an  optical  instrument 
alone,  but  with  an  organ  of  sense  as  well.  All  of  our  senses 
are,  in  a  measure,  affected  by  education,  and  after  a  certain 
habit  has  been  once  firmly  fixed  it  is  with  difficulty  changed  in 
any  important  particulars.  It  is  a  fact  now  generally  ac- 
knowledged that  when  strabismus  has  existed  for  a  great 
while,  binocular  vision  is  not  obtained  even  after  the  optical 
axes  are  correctly  placed  by  an  operation. 

It  has  seemed  to  me,  therefore,  not  only  unwise,  but  useless 
to  attempt  to  force  eyes  back  to  our  conventional  standard, 
and  to  insist  on  patients  wearing  glasses  giving  full  correction, 
when  a  fair  trial  has  proven  their  unsatisfactoriness.  Under 
these  circumstances,  it  would  appear  best  to  find  the  glass, 
generally  a  weak  one,  which  gives  most  comfort  and  tenta- 
tively increase  the  strength. 

The  case  just  related  also  well   demonstrates    the    condition 


DIFFICULTY    IN    WEARING    CORRECTING    GLASSES.  165 

commonly  called  "  spasm  of  accommodation."  There  was  a 
much  higher  refraction  manifest  before  the  action  of  the 
atropine  than  after,  and  this  is  usually  attributed  to  a  spasm 
of  the  ciliary  muscle.  If  by  "  spasm  "  is  meant  a  permanent 
tonic  contraction  of  the  muscle,  the  term  is  certainly  misap- 
plied, since  when  there  is  nothing  to  call  the  accommodation 
into  play  the  muscle  is  relaxed,  as  shown  by  the  direct  ophthol- 
moscopic  examination.  The  unusual  contraction  of  the  cil- 
iary muscle  in  this  case  is,  in  my  opinion,  a  voluntary  act,  and 
is  due  to  the  fact  that  the  patient  from  custom  or  preference 
has  always  used  her  anterior  focal  plane,  which  would  necessi- 
tate such  a  contraction  of  the  ciliary  muscle  as  shall  convert  a 
H.  astig.  axis  90°  to  a  M.  astig.  of  the  same  degree  axis  180°. 
The  use  of  this  plane  has  become  a  fixed  habit  with  her  and 
the  probabilities  are  that,  at  her  time  of  life,  it  can  be  broken 
up  with  difficulty  or  not  at  all.  Such  difficulties  as  these  are 
much  less  frequent  in  younger  people  who  can  more  readily 
adapt  themselves  to  altered  conditions. 

Another  aggravated  case  of  this  character  is  the  following  : 

CASE  VII.  A  lady,  42  years  old,  had  been  treated  for  asthenopia  by  Dyer's  method 
for  some  months,  without,however,the  discovery  being  made  of  any  refractive  anomaly. 
A  Philadelphia  surgeon,  to  whom  she  applied  later,  worked  out,  under  atropine,  a 
high  degree  of  astigmatism  which  I  found  to  agree  essentially  with  that  diagnosed 
by  myself.  The  data  obtained  by  the  keratometer of  Javal  were:  L,  15°  /f=73/4  mm. 
i85°  =  81/4  mm.  with  a  crossing  of  3*1/2 steps;  R.  75° K=£l/tmm.  i6o°=71/2mm.  with 
"a  crossing  of  4*/2  steps.  V  without  glasses  =  4/eo  in  L.,  less  than  that  in  R.  With 
—3.5"*  15°,  L  V=Vis,  with— 4.5  70°  R  V=Vi»- 

The  Philadelphia  surgeon  had  ordered  correcting  glasses,  with  instructions  to 
persevere  in  their  use.  This  she  had  done,  but  the  longer  she  wore  them  the  more 
uncomfortable  they  became.  They  made  her  so  dizzy  that  she  was  utterly  unable 
to  wear  them  in  the  street,  and  she  could  not  read  with  them  at  all.  She 
was  then  ordered  glasses  which  would  combine  a  +1.5  with  the  correction  above 
indicated,  with  the  hope  that  thereby  she  would  be  able  to  use  her  eyes  for  near 
work  at  least,  and  in  time  work  her  way  gradually"  to  full  correction  for  distance.  It 
was  because  she  found  that  after  several  months'  trial  it  would  not  be  possible  to 
use  either  of  these  with  benefit  or  even  comfort,  that  application  was  made  to  me. 
With  this  experience  before  me  I  had  not  much  hope  of  benefiting  her  by  means  of 
glasses,  particularly  as  I  suspected  that  a  large  part  of  the  asthenopia  was  nervous. 
I  gave  for  experimental  use,  L  -(-3.5  105°,  R  +4.5  160°,  to  be  used  for  near  work. 
She  could  read  with  comfort  for  a  somewhat  longer  time  with  these  than  without 
them,  but  the  benefit  was  not  at  all  encouraging. 


i66 


DEFICIENCY    IN    CORRECTING    BY    CYLINDERS. 


§  189.  Do  cylinders  give  an  absolute  correction  of  the  as- 
tigmatic condition  ?  They  can  not,  from  the  fact  that  the  re- 
fraction of  an  elliptical  surface  cannot  be  neutralized  by  a 
surface  which  has  equal  radii  of  curvature. 

Fig.  44. 


A 


EFFECT  OF  A  CYLINDRICAL  LENS  ON  THE  REFRACTION  OF  THE  SHARPER  KM> 
OF  AN  ELLIPSOID  WHEN  THE  PERIPHERAL  RAYS  OF  THE  TWO  MERIDIANS  ARE 
BROUGHT  TOGETHER. 

§  190.  Where  the  cornea,  as  it  usually  does,  represents  a 
triaxial  ellipsoid,  we  have  a  different  set  of  conditions  accord- 
ing to  the  special  character  of  the  curvature ;  and  the  action  of 
cylindrical  lenses  on  the  refraction  of  the  principal  meridians 
will  not  be  uniform  in  all  cases. 

Let  us  take,  as  an  example,  that  form  in  which  the  cornea 
represents  the  sharper  end  of  an  ellipsoid  with  three  unequal 
axes.  It  is  plain  from  what  has  been  demonstrated  in  Chapter 
II  that  the  meridian  of  greater  curvature,  should  it  pass  a 
certain  point,  will  suffer  from  the  greater  aberration.  A  in  fig. 
44  represents  the  meridian  of  less,  and  B  the  meridian  of 
greater  cuivature.  In  A,  the  peripheral  ray  d  crosses  the 
principal  axis  XX'  at  e  and  the  more  central  ray  b  at  a,  while 
in  B  the  corresponding  ray  d'  crosses  at  /,  and  b'  at  k.  If  we 
place  a  cylindrical  lens  before  the  refracting  surface  with  its 
curvature  corresponding  to  the  meridian  B,  and  of  such 


DEFICIENCY    IN    CORRECTING    BY    CYLINDERS. 


i67 


strength  that  the  peripheral  ray  d'  is  carried  back  and  made  to 
cross  the  axis  in  the  same  point  e  as  the  peripheral  ray  d  of 
the  meridian  A,  the  relation  between  k  and  z,  though  they  are 
both  carried  back  from  their  original  position,remains  unaltered 
at  c  and  e,  since  the  regular  refraction  of  the  cylinder  does  not 
counteract  the  aberration  of  the  elliptical  surface.  The  result 
would  be  that  the  rays  crossing  at  a  and  c,  would  form  figures 
of  diffusion  on  the  focal  plane  passing  through  e. 


45- 


I  a 


r, 


ANOTHER  EFFECT  OF  A  CYLINDRICAL  LENS  ON  THE  REFRACTION  OF  AN  ELLIPSOID 
WHEN  THE  PERIPHERAL  RAYS  OF  THE  Two  MERIDIANS  ARE  BROUGHT  TO- 
GETHER. 

/ 

If  we  bring  the  more  peripheral  rays,  d  and  d ',  of  the  two 
meridians,  A  and  B,  to  cross  at  the  same  point  c,  moving  them 
forward  from  a,  z,  as  in  fig.  45,  we  have  the  same  result;  for 
the  central  rays  b,  b' ,  which  cross  the  axis  at  e  and  k,  would 
form  figures  of  diffusion  on  the  focal  plane  passing  through  c. 

§  191.  We  would  have,  of  course,  an  analogous  state  of  af- 
fairs in  dealing  with  the  blunter  end  of  the  ellipsoid ;  for  while 
it  would  be  possible,  by  means  of  a  cylindrical  lens,  to  bring 
corresponding  peripheral  or  central  rays  to  cross  the  axis  at 
the  same  point,  it  would  not  be  possible  to  bring  both  the  cen- 


168 


DEFICIENCY    IN    CORRECTING    BY    CYLINDERS. 


tral  and  peripheral  rays  to  cross  it  in  one  point ;  and  it  we 
should  have  to  deal  with  a  surface  in  which  one  meridian  rep- 
resented the  blunter  end  of  an  ellipse,  while  the  other  repre- 
sented the  sharper  end,  the  diffusion  figures  would  be  still 
more  confusing.  Fig.  46  represents  such  a  surface  where  the 
peripheral  rays,  d,  d',  are  brought,  by  means  of  a  cylinder,  to 
cross  the  axis  at  the  same  point  e.  The  more  central  ray  b  of 
the  flatter  ellipse  A,  will  cross  the  axis  at  c,  behind  the  focal 
plane,  passing  through  e,  while  the  more  central  ray  b'  of  the 
sharper  ellipse  B,  will  cross  it  in  front  at  a,  thus  forming  two 
sets  of  diffusion  figures. 

Fig.  46. 


REFRACTION 


BY    THE    BLUNTER  AND  SHARPER  ENDS  QF   AN   ELLIPSOID  COR- 
RECTED  BY  A  CYLINDER. 


§  192.  Under  any  of  these  forms  which  the  cornea  may  as- 
sume,1 the  retinal  image  must  have  its  distinctness  of  outline 
impaired  by  the  circles  of  diffusion  which  fall  on  it.-  This  dif- 

1  In  all  the  measurements  that  have  been  made  up  to  the  present  time,  the  cornea 
has  never  been  found  to  assume  in  either  of  its  principal  meridians  the  form  of  the 
blunter  end  of  ellipse,  but  we  see  no  reason  to  doubt  the  possibility  of  such  an 
occurrence. 

*We  do  not  take  into  consideration  here  the  rays  passing  thu  ugh  the  intermediate 
meridians.  These  require  a  separate  investigation. 


EFFECT    OF    CYLINDERS    ON    THE    NODAL    POINTS.  169 

fusion  being  greater  in  the  higher  than  in  the  lower  forms  of 
astigmatism,  we  should  expect  to  find  the  visual  acuteness, 
after  all  possible  correction,  less  in  the  former,  and  such  I  be- 
lieve is  the  experience  of  all  practitioners.  We  should  also 
expect  that  the  vision  of  astigmatics,  after  correction,  would 
be  less  than  that  of  myopes  and  hypermetropes  of  the  same 
grade  after  their  neutralization  by  spherical  lenses. 

As  a  matter  of  statistics,  I  find  that  out  of  about  2,000  as- 
tigmatic eyes  of  all  degrees,  only  about  \/{0  have  V=i,  after 
the  best  possible  correction. 

§  193.  It  is  apparent  that  this  aberration  in  the  principal 
meridians  will  be  greater,  the  greater  the  angular  aperture — 
which  in  the  eye  would  be  represented  by  the  pupil — and  con- 
sequently the  larger  the  pupil  the  larger  the  figures  of  diffu- 
sion, and  the  more  indistinct  the  retinal  image. 

This  is  an  additional  reason  for  not  accepting  the  examina- 
tions made  under  atropine  as  absolute,  since  the  effect  of  the 
diffusion  images  on  the  retina  will  be  different  with  a  large 
pupil  and  with  one  of  normal  size,  and  this  difference  is  likely 
to  be  strongly  felt  in  the  final'correction. 

§  194.  Another  point  in  the  action  of  cylinders  to  be  taken 
account  of  in  this  connection  is  their  influence  on  the  position 
of  the  nodal  points  in  the  meridian  of  their  action.  While  the 
cylinder  in  correcting  the  abnormal  refraction  brings  the  focal 
points  of  the  two  meridians  together  approximately,  it  ad- 
vances the  nodal  points  of  the  meridian  it  affects  when  it  is  con- 
vex, and  causes  them  to  recede  when  it  is  concave.  Now,  the 
size  of  the  retinal  image  is  governed  by  the  position  of  the 
nodal  points  in  relation  to  the  retina.  This  image  is  larger  for 
the  same  object  the  farther  the  nodal  points  are  removed  from 
it.  We  should,  consequently,  expect  to  find  a  diminution  of 
the  image  on  account  of  the  recession  of  the  nodal  points, when 
a  concave  cylinder  is  used,  in  the  direction  of  the  faulty  meri- 
dian, and  an  enlargement  of  it  in  the  direction  of  the  hyperme- 
tropic  meridian  when  a  convex  cylinder  is  used.  As  a  result, 
there  would,  theoretically,  be  an  enlargement  of  an  object  in 
the  direction  of  the  meridian  corrected  by  a  +  cylinder,  and  a 


I7O       HOW    LOW    A    DEGREE    OF    ASTIG.   IS    TO    BE    CORRECTED. 

diminution  of  it    in  the   direction  corrected   by  a — cylinder. 

§  195.  How  low  a  degree  of  astigmatism  it  is  necessary  to 
correct?  This  is  not  purely  a  question  in  optics,  but  one  in 
answering  which  many  considerations  must  enter. 

Cylindrical  glasses  should  not  always  be  prescribed 
simply  because  distant  vision  as  tested  by  the  test  types 
is  thereby  rendered  better,  for  some  persons  with  an  as- 
tigmatism of  0.75  D  have  a  sharpness  of  sight  for  distant  ob- 
jects, on  account  of  their  better  interpretation  of  retinal  impres- 
sions, superior  to  some  whose  eyes  are  emmetropic.  If  such  per- 
sons are  satisfied  with  their  distant  vision,  and  do  not  suffer,  no 
good  can  result  from  forcing  on  them  the  constant  use  of  glasses. 
The  use  of  glasses  is  a  great  inconvenience,  many  persons  are 
strongly  prejudiced  against  them,  and  they  are  more  or  less 
expensive.  The  wearing  of  weak  glasses  should,  therefore, 
not  be  made  imperative,  if  decided  objection  is  urged,  unless 
the  surgeon  is  satisfied  that  undoubted  benefit  will  follow  their 
use. 

But  when  there  is  a  complaint  of  asthenopia,even  when  the  eyes 
are  not  used  at  close  work,  and  particularly  in  nervous  women, 
the  correction  of  even  low  degrees  of  astigmatism  is  usually 
attended  with  great  benefit.  The  constant  use  of  cylinders 
of  O.5D  is  often  sufficient  to  transform  misery  into  com- 
fort. And  in  almost  all  cases  the  addition  of  a  0.50  cyl- 
inder, where  it  is  required,  to  presbyopic  glasses  makes  reading 
much  more  comfortable,  in  the  evening  especially,  or  where 
close  application  for  a  considerable  time  is  necessary. 

It  occasionally  happens,  too,  that  the  correction  of  astigma- 
tism as  low  as  0.25  D  is  found  very  beneficial.  Such  cases  are 
usually  iound  in  persons  whose  nervous  systems  are  below 
par,  and  on  restoration  to  health  the  glasses  can  be  laid 
aside. 

When  the  amount  of  astigmatism  after  cataract  extraction 
exceeds  iD  there  is  always  an  advantage  from  its  correction; 
for  less  degrees  it  is  hardly  worth  while. 

§  196.  We  would  call  attention  here  to  a  fact  in  the  correc- 
tion of  astigmatism  which  has  not  yet  met  with  a  satisfactory 


HOW    TO    PROVE    GLASSES.  17! 

explanation,  and  that  is  the  improvement  in  vision  given  by  the 
tilling  of  a  spherical  lens  superior  to  that  afforded  by  a  cylin- 
der equivalent  to  that  amount  of  inclination  of  the  spherical. 
It  is  a  matter  of  common  observation  that  persons  operated  on 
for  cataract  often  see  better  when  their  spectacles  are  held  ob- 
liquely. This  difference  in  effect  may  be  due  to  some  differ- 
ence of  action  on  the  rays  passing  through  the  intermediate 
meridians,  a  subject  which  has  not  been  fully  examined  into 
on  account  of  the  great  difficulty  in  obtaining  formulae  of  gen- 
eral application. 

It  may  also  be  stated,  in  this  connection,  that  some  astigma- 
tics  can  correct  their  anomaly  appreciably  by  making  pressure 
at  the  proper  place  on  the  sclera*  to  give  the  correcting  curva- 
ture to  the  cornea  in  that  meridian. 

§  197.  When  a  prescription  for  glasses  has  been  given,  the 
case  should  not  be  summarily  dismissed.  The  patient  should 
be  instructed  to  bring  the  glasses  back  for  examination,  for  it 
is  of  the  greatest  importance  that  the  optician  shall  have  fol- 
lowed strictly  the  instructions  of  the  surgeon.  An  approxima- 
tion to  the  glasses  ordered  will  by  no  means  suffice.  A  small 
error  in  the  number  of  the  lens,  or  a  change  of  2°  or  3°  in  the 
position  of  the  axis  of  the  cylinder  will  often  mar  an  otherwise 
good  result.  The  mistake,  moreover,  may  not  always  be  the 
opticians.  In  the  hurry  of  many  examinations  the  surgeon 
himself  may  have  put  down  the  wrong  number  or  the  wrong 
degree,  or  put  L  for  R.  The  necessity  of  some  method  of 
proving  glasses  is  therefore  apparent. 

§  198.  There  are  several  methods  by  which  this  may  be  done 
but  the  one  which  is  most  rapid  and  best  adapted  to  the  con- 
sultation room  is  that  of  neutralization. 

When  a  -f-  and  —  lens  are  placed  together  the  action  of  the 
one,  as  is  well  known,  tends  to  neutralize  that  of  the  other,  so 
that  the  combined  power  of  the  two  is  always  equal  to  the 
difference  in  their  refraction.  When  the  strength  of  the  two  is 
the  same,  their  optical  action  will  be  nil,  the  same  as  a  bit  of 
plane  glass.  When,  therefore,  we  find,  for  example,  a  —  lens 
whose  power  we  know  which  completely  neutralizes  a  +  lens* 


1/2  HOW    TO    PROVE    CYLINDERS. 

the  power  of  which  we  did  not  know,  the  number  of  the  one 
gives  us  the  number  of  the  other. 

How  shall  we  know  when  the  one  neutralizes  the  other?  One 
very  simple  method  is  that  of  watching  the  paralactic  move- 
ment of  objects  through  them. 

When  a  convex  lens  is  moved  back  and  forth  a  few  inches 
before  the  eye,  and  at  right  angles  to  the  optical  axis,  objects 
seen  through  it  are  observed  to  move  in  a  direction  opposite  to 
that  of  the  lens.  Through  a  concave  lens  the  movement  is  in 
the  same  direction  as  that  of  the  lens. 

Let  us  have,  for  example,  a  —  lens  whose  number  we  are  ig- 
norant of  and  the  exact  refracting  power  of  which  we  wish  to 
find.  If  the  large  types  of  Srrellen  are  very  indistinct  through 
it,  we  know  at  once  that  it  is  a  strong  glass,  and  begin  by  plac- 
ing on  it  a  strong  -f-  glass,  say  No.  4.  With  this  most  of  the 
letters  of  the  test-types  are  seen,  but  there  is  still  a  movement 
of  objects  "  with  "  the  lens.  With  a  +  5,  there  is  a  slight 
movement  of  the  letters  '•  against  "  that*  of  the  lens,  showing 
an  excess  of  -(-  action.  No.  4  is,  therefore,  too  weak,  and  No. 
5  too  strong.  We  now  try  +  4.5  and  find  that  in  whatever  di- 
rection the  combined  lenses  are  moved  objects  remain  station- 
ary. It  is  possible  by  this  test  to  tell  to  within  0.25  D  the  pow- 
er of  any  spherical  lens,  and  this  is  sufficiently  accurate  for  all 
practical  purposes. 

§  199.  The  question  becomes  somewhat  more  complicated, 
however,  when  cylinders  are  to  be  dealt  with,  because  in  them 
we  have  to  determine  not  only  the  strength  of  the  lens,  but  also 
the  direction  of  its  axis.  In  this  examination  we  employ  the 
fan  of  Snellen. 

Example :  The  lens  whose  power  is  to  be  determined,  is  a 
sphero-cylindrical  convex.  Through  it  the  whole  of  Snellen's 
fan  is  indistinct.  But  by  holding  in  front  of  it  concave  spheri- 
cals,  one  after  the  other,  a  lens  is  finally  found  which  shows 
the  line  at  20°  clear  and  sharp.  The  concave  lens  which  gives 
the  neutralization  is  of  course  the  weakest  one  through  which 
this  line  appears  with  clearly  defined  edges  and  which  gives  no 
paralactic  movements.  If  this  is  —  2.5,  then  we  know  that  the 


HOW    TO    PROVE    CYLINDERS.  1/3 

meridian  of  the  sphere-cylinder  whose  axis  is  at  2O°  is  +  2.5. 
But  with  this,  the  lines  to  the  right  of  the  center  of  the  fan  are 
still  blurred  and  offer  paralactic  movements.  We  now  try  the 
addition  of  concave  cylinders  with  their  axis  at  no0,  that  is  in 
the  direction  of  the  blurred  lines,  until  one  is  found  which 
renders  the  fan  uniform  and  clear.  When  these  lenses  are 
moved  together  there  will  be  no  paralactic  action  if  the  correc- 
tion has  been  complete.  Should  there  be  a  movement  of  objects 
it  must  be  noted  whether  it  is  in  the  direction  of  the  cylinder's 
axis  or  at  right  angles  to  it  or  in  both  directions,  and  of  course 
also  whether  "  with  "  or  "  against "  the  lenses.  If  there  is  a 
movement  when  the  lenses  are  moved  parallel  to  the  direction 
of  the  axis  of  the  cylinder,  then  the  spherical  lens  is  not  right. 
If  there  is  no  movement  in  this  direction,  but  only  at  right 
angles  to  the  axis  of  the  cylinder,  then  the  cylinder  is  at  fault, 
and  the  lens  in  either  case  will  have  to  be  increased  or  dimin- 
ished in  power  according  to  the  direction  of  the  movement,  un- 
til one  is  found  with  which  all  movement  ceases. 

§  200.  Dr.  E.  Gruening,  of  New  York,1  employs  a  method  of 
"simultaneous  contrast"  which  he  has  found  very  convenient, 
and  which  he  prefers,  as  being  more  accurate,  to  the  one  just 
described. 

When  a  narrow  stripe  of  a  marquetry  floor  or  carpet  is 
looked  at  through  a  convex  lens,  that  part  seen  through  the 
lens  appears  wider  than  the  part  lying  to  either  side  of  it;  when 
viewed  through  a  concave  lens  it  appears  narrower.  As  the 
margins  of  the  stripe  inside  and  outside  the  lens  are  seen  at  the 
same  time  coming  up  to  the  edge  of  the  lens,  a  small  differ- 
ence in  magnitude  can  be  readily  detected.  In  applying  this 
principle  to  the  testing  of  spherical  glasses  we  have  only  to  hold 
the  lens  to  be  proven  horizontally  parallel  with  the  floor  and, 
looking  down  through  it  at  the  stripe,  observe  whether  the  part 
seen  through  the  lens  is  larger  or  smaller  than  that  lying  out- 
side of  it.  If  it  is  larger  the  lens  is  convex  and  we  apply  con- 
caves, as  in  the  preceding  experiment,  until  the  stripe  is  con- 

1  Verbal  communication. 


1/4  HOW    TO    PROVE    CYLINDERS. 

tinuously  of  the  same  size  from  both  sides  through  the  lens. 
If  the  part  seen  through  the  lens  is  narrower,  there  is  an  excess 
of  minus  action,  and  we  apply  convex  lenses  until  one  is  found 
which  gives  a  uniform  stripe. 

The  same  principle  holds  good,  of  course,  for  cylinders  when 
their  axes  lie  in  the  same  direction  as  the  stripe.  In  the  meri- 
dian perpendicular  to  the  stripe  they  act,  to  all  intents  and  pur- 
poses, as  sphericals,  and  may  be  so  considered.  If,  therefore, 
the  stripe  is  seen  through  the  cylinder,  in  this  position,  to  be 
enlarged,  there  is  a  plus  action,  and  it  is  corrected  by  placing 
a  concave  cylinder  on  it  with  its  axis  coinciding  with  the  stripe 
and  the  axis  of  the  lens  to  be  tested  ;  if  it  is  diminished  in  size 
there  is  an  excess  of  minus  action,  and  the  correction  is  made 
by  convexes,  applied  in  a  similar  manner. 

But  the  method  is  likewise  useful  in  determining  the  direc- 
tion of  the  cylinder's  axis.  The  portion  of  the  stripe  seen 
through  the  cylinder  and  the  portions  outside  of  it  do  not  run 
in  the  same  direction  except  when  the  stripe  and  the  axis  of 
the  cylinder  coincide  or  are  at  right  angles  to  each  other.  Any 
deviation  from  these  two  positions  causes  the  two  portions  to 
lie  at  angles  to  each  other.  Knowing  the  angle  at  which  the 
axis  of  the  cylinder  should  be,  and  finding  the  angle  at  which 
it  is  necessary  to  place  the  lens  to  be  determined  in  order  that 
the  parts  within  and  without  the  lens  fall  in  the  same  direction, 
we  here  have  the  necessary  data  for  determining  whether  the 
axis  is  properly  placed. 

BIBLIOGRAPHY. 


Airy,  George  Biddell — On  a  peculiar  defect  in  the  eye  and  a  mode  of  correcting  it 
Trans.  Camb.  Philos.  Soc.  V.  II.  1827.  P.  267-271.  (Read  Feb.  21,  1825). 

Airy,  G.  B.— (Cylindrical  glasses).     Ed.  Jour,  of  Sci.     No.  XIV.     P.  322. 

Bagnesis — Emploi  d.  verres  correcteurs  en  ophthalmol.     Ths.  de  Paris,  1883. 

Burnett.  S.  M. — Refract,  in  the  principl.  mends,  of  a  triax.  ellipsoid,  with  rrnks.  on 
the  correct,  of  astig.  by  cyld.  glasses,  and  an  histor.  note  on  corn,  astig.  with  a  com- 
municat.  on  the  monochrom.  aberrat.  of  the  hum.  eye  in  aphakia.  by  Prof.  \V.  Hark- 
ness.  Arch.  Ophth.  XII.  Pp.  I-2I.  N.  Y.  1883. 

Carter,  R.  B. — On  defects  of  vis.  which  are  reined,  by  optic,  appliances.  Med. 
Times  and  Gaz.  I.  VI.  July,  Aug.  and  Sept  1877. 


BIBLIOGRAPHY. 


1/5 


Bonders,  F.  C. — Anomalies  of  the  accommodation  and  refraction  of  the  eye.  New. 
Syd.  Soc.  Lond.  1864. 

Bonders,  F.  C.— Astig.  en  cylindrsch.  glazen.  Utrecht,  1862.  Germ,  transl.  by 
Schweiger.  H.  Peters.  Berlin,  1862.  Fch.  transl.  by  H.  Bor.  Paris,  1863. 

Bonders,  F.  C.— Prakt.  Bermerk.  ueberden  Einfluss  v.  Hulfslinsen  auf  die  Sehsc- 
harfe.  Graefes  Arch.  XVIII-1I.  P.  245.  1872. 

Farley,  C.  II,— A  method  of  discover,  and  correct,  astig.  Bost.  Med.  and  Surgjr. 
June  13.  1872. 

Galezowski — Tabl.  synopt.  de  la  refract,  de  1'oeil;  choix  des  lunettes.  Paris 
1865. 

Gosetti — L'asthenop.  sua  patogen.  e  cura.  Annal.  di.  Ottalm.  XII.  Pp.  3-4 
1884. 

Green  John — On  spectacle  lenses  of  asymmetrical  curvature.  Amer.  Jnl.  Oph. 
Mch.  1886,  pp.  53 — 59. 

Homberger,  J. — Astig.  and  cylnd.  glasses.  A  review  of  Bonder's  theories.  Am 
J.  Ophth.  II.  Pp.  21-65.  N-Y-  l864- 

Hay,  G. — Befcts.  of  ocul.  refract,  accommod.  and  converg.  and  their  treatment  by 
spectls.  and  otherwise.  Bost.  Med.  and  Surg.  Jr.  Oct.  20.  1870. 

Imbert,  A. — Nouveau  precede  de  verification  des  verres  cylindriques.  Ann.  d'Ocul. 
Mai.  Juni.  1885. 

Javal,  E. — Sur  le  choix  d.  verres  cylind.     Ann.  d'Oculist.     LI  1 1.     P.  50.     1865. 

Javal,  E. — Be  la  neutraliz.  d.  1'ache  de  la  vis.  Ann.  d'Oculist.  LIV.  P.  9. 
1865. 

Javal  E. — Sur  le  choix  d.  verres  cylind.    Ann.  d'Oculist.     LV.     P.  5.     1866. 

Javal,  E. — Sur  les  applicat.  d'un  appareil  nouveau  destine  a  measur.  1'astig.;  an- 
alyse mathemat.  de  1'  act.  d.  verres  cylind.  Cong,  internat.  de  Geneve.  1877. 

Knapp,  H. — Ueber  d.  Einfluss  d.  Brillen  auf  die  optisch  Constanten  u.  die  Seh- 
scharfe  des  Auges.  Arch.  f.  Augen.  u.  Ohrenhlk.  I.  2.  1870. 

Knapp,  H. — On  the  designation  of  the  meridians  in  the  determination  of  glasses 
and  of  the  visual  field.  Archives  of  Oph.  XV.,  pp.  207 — 210.  1886. 

Konigstein — Bie  Anomal.  d.  Refct.  u.  Accommodat.  Practische  Anleiting  zur 
Brillen  bestimmung.  Wien.  1883. 

Laurence,  J.  Z. — On  astig  and  its  correct,  by  cylind.  lenses.  Med.  Mirror.  I.  Pp. 
4-11.  London.  1864. 

Levi,  M. — Saggio  pratic.  sull  'astig.  e  metodo  facile  per  trov.  la  correz.  Ann.  di 
Ottal.  VII.  Pp.  232  47.  Milan.  1878. 

Loring,  E.  G. — An  astig.  glass  for  catarct  patients.  Trans.  Amer.  Ophth.  Soc. 
Pp.  108-18.  1871. 

Mauthner,  L. — Vorlesungen  ii  d.  optisch.  Fehler  d.  Auges.  Wien.  W.  Braumiil- 
ler.  1876. 

Motais — I 'ince-nez  pour  verres  cylindriques.     Ann.  d'Ocul.    Mai.  Juni.     1885. 

Noyes,  H.  B. — Note  respect,  the  first  recorded  case  of  astig.  in  this  country  for 
which  cylind.  glasses  were  made.  Am.  Jr.  Med.  Soc.  N.  S.  LXIII.  Pp.  355-9- 
1872. 

Raehlmann,  E. — Ueber  die  optische  Wirk.  d.  hyperbol.  Linsen.  Ber  Anwend. 
derselb.  als  Brillen.  Zehenders  Monatsbl.  XX.  P.  III. 

Raehlmann— Glaesercorrect.  bei    Keratocon.     Ber.    ii    d.  versamml.    d.    Ophth. 


1/6  BIBLIOGRAPHY. 

Gesellsch.    XII.     Pp.  50-2.     Stuttg.     1879. 

Reusch,  F.  E. — Theorie  der  Cylinderlinsen,  p.  35.     Leipsig,  1868. 

Reynolds,  D.  S. — The  prolate  lens  of  Dr.  Fox. — Mr.  Borsh's  sphere-cylinders  on 
one  surface.  Amer.  Jn'l  Oph.  April,  1886,  pp.  95 — 98. 

Roberts,  P.  F. — Prescrip.  de  lente*  en  un  caso  de  astenop.  acomodat.  pra  astig. 
compust  y.  anisometroe.  Rev.  Med-quir.  XVI.  Pp.  198-204.  Buenos  Ayres. 
1878-9. 

SchiStz — A  case  of  astigmatism  of  the  lens  after  iridectomy.  Archives  of  Oph. 
XV.,  pp.  200—203.  1886. 

Schidtz,  H. — On  the  most  suitable  metho  1  of  recording  optometric  examinations. 
Archives  of  Oph.  XV.,  pp.  203 — 207.  1886. 

Schweigger,  C. — Bemerk.  ii.  die  Diag.  u.  Correct  d.  Astig.  Arch.  f.  Ophth.  IX. 
Hft.  I.  Pp.  178-91.  Berlin.  1863. 

Stilling,  J. — Sphaerold.  Glaeser.  gegen  Astig.  Centralb.  f.  prakt.  Augenhlk.  IV. 
Pp.  273-5.  Leipzig.  1880. 

Woinow — Ein  kurze  Bemerk.  zum  Brillen  gebrauch.  Graefes  Arch.  XVIII.  Abt. 
II.  P.  49.  1882. 

Woinow — Zur  Lehre  U  den  Einfluss  d.  optisch  Glaeser  auf  die  Sehscharfe.  Graefes 
Arch.  XVIII.  Abt  I.  P.  349.  1872. 


CHAPTER   XIII. 


IRREGULAR  ASTIGMATISM — CONICAL  CORNEA. 

§  20 1.  Regular  astigmatism,  as  we  have  seen,  is  a  condition 
of  the  eye  in  which  its  refraction  approaches  that  of  a  triaxial 
ellipsoid  where  the  principal  meridians  are  ellipses  and  at  right 
angles  to  each  other.  All  other  departures  from  a  strictly 
spherical  refraction  are  classed  under  the  general  term — irregu- 
lar astigmatism. 

§  202.  IRRE.GULAR  ASTIGMATISM  can  have  its  seat  in  either 
one  of  the  refracting  media  of  the  eye  and  may,  consequently, 
be  lenticular  or  corneal. 

§  203.  With  very  rare  exceptions  all  eyes  are  affected  with  a 
certain  amount  of  irregular  astigmatism,  but  when  it  is  not 
sufficient  to  reduce  V  below  20/20,  it  is  considered  as  normal. 

Normal  irregular  astigmatism  is  for  the  most  part  lenticular 
and  is  the  result  of  a  want  of  homogenity  in  the  lens  substance. 

This  want  of  uniformity  of  structure  is  due,  mainly,  to  the 
manner  of  the  lens's  growth.  The  development  of  the  lens  is 
not  symmetrical  in  its  entirety,  but  in  parts  or  sectors  inde- 
pendent of  one  another  and  these  are  afterwards  joined  to- 
gether to  constitute  a  whole.  It  is  seldom  that  the  union  of 
these  sectors  is  so  perfect  as  to  leave  no  trace  of  their  separ- 
ate existence. 

§  204.  This  peculiarity  in  the  construction  of  the  lens  is  dem- 
onstrated by  dissection  and  by  entoptic  experimentation. 

Anatomical  investigation  shows  not  only  a  gradual  increase 
in  the  density  of  the  lens  substance  from  the  circumference  to- 
wards the  center,  but  also  the  remains  of  its  sectorial  evolu- 

(177) 


1/8  SECTOIRAL    CONSTRUCTION    OF    THE    LENS. 

tion.  Fig.  47  is  a  meridional  section  of  the  lens  of  a  young 
infant  in  which  this  sectorial  character  is  well  represented. 
This  structure  of  the  lens  is  also  often  apparent  in  the  liv- 
ing eye  under  oblique  illumination,  and  particularly  so  in  some 
cases  of  cataract,  where  the  line  of  union  of  two  adjacent  sec- 
tors is  plainly  visible. 

§205.  The  refractive  unevenness  of  the  lens  caused  by  its 
anatomical  structure  is  shown  by  means  of  a  simple  entoptical 
experiment.  Make  a  fine  point  of  light  by  holding  a  strong 
convex  lens,  such  as  the  ocular  of  a  "microscope,  at  ten  or 

Fig -47- 


w 

^-4 A  \  \     '•     .'•''" 
THE  SECTORIAL  CONSTRUCTION  OF  THE  HUMAN  CRYSTALLINE  LENS. 

twelve  feet  from  a  gas  jet.  In  this  manner  a  fine  pencil  of  rays 
is  obtained  which  we  can  use  for  casting  on  the  retina  shadows 
of  such  opaque  objects  in  the  refracting  media  of  the  eye  as  lie 
in  its  path,  while  variations  in  density  will  manifest  themselves 
by  brighter  or  darker  lines  or  spots.  As  this  bright  focus  is 
approached  to  the  eye  we  see  first,  the  shadows  cast  by  the  ob- 
jects on  the  surface  of  the  cornea,  such  as  tears,  meibomian  se- 
cretions, etc.  As  it  is  brought  closer,  the  diffraction  of  the 
pupillary  edge  of  the  iris  is  seen,  and  then  the  inequalities  of 
the  lens  structure,  those  on  the  anterior  face  being  first  brought 
to  view,  afterwards  those  at  the  center  and  on  the  posterior  face 


SPECTRUM    OF    THE    LENS.  1/9 

successively  ;  and  finally  the  objects  in  the  vitreous  humor  and 
on  the  inner  layers  of  the  retina.  A  "  spectrum"  of  the  crys- 
talline lens  thus  obtained  shows  such  a  want  of  homogeneity 
of  structure  as  would  not  be  tolerated  in  any  optical  instru- 
ment of  man's  construction.  Bonders  gives  at  page  200  of  his 
"Treatise  on  the  Anomalies  of  Refraction  and  Accommodation 
of  the  Eye  "  a  very  elegant  spectrum  of  the  crystalline  lens  of 
his  right  eye.  In  Fig.  48  is  given  a  diagram  of  the  spectrum 
of  my  right  eye,  showing  the  remains  of  the  lines  of  union  of 
the  sectors  ;  the  minor  irregularities  in  the  structure  of  the  lens 
are  not  recorded  in  the  diagram. 

Fig.  48. 


A  SPECTRUM  OF  THE  AUTHOR'S  CRYSTALLINE  LENS,  SHOWING  THE  LINES  OF 
UNION  OF  THE  SECTORS. 


§  206.  It  is  a  legitimate  inference  that  such  optical  imperfec- 
tions should  seriously  impair  visual  acuteness,  and  this  un- 
doubtedly is  the  case.  It  is  certain  that  our  conventional 
standard  of  visual  acuteness  would  be  much  higher  than  20/2o  if 
it  were  not  for  these  defects  in  the  lens,  and  it  is  most  proba- 
ble that  to  a  freedom  from  them  is  to  be  attributed  that  super- 
normal acuteness  possessed  by  some  persons — amounting  often 
to  2%0. 

We  have,  however,  become  so  accustomed  to  many  of  the 
manifestations  of  these  defects,  that  we  either  ignore  them  or 
no  longer  regard  them  as  abnormal. 


ISO          CAUSE  OF  THE  RADIATIONS  OF  A  STAR. 

§  207.  The  most  common  of  these  appearances  are  the  lines 
seen  radiating  from  bright  stars  or  distant  points  of  light.  We 
are  perfectly  well  aware  that  the  stars  are  in  reality  not  rayed, 
but  round,  and  yet  so  wide  spread  is  this  fault  of  vision  that 
the  conventional  typical  representation  of  a  star  has  become  to 
be  a  central  bright  spot  with  radiating  bright  streaks. 

Fig.  49. 


THE  APPEARANCE  OF  A  DISTANT  POJNT  OF  LIGHT  TO  THE  AUTHOR'S 

RIGHT  EYE. 

Only  a  very  few  persons  are  recorded  as  seeing  the  stars 
without  these  rays,  from  which  we  may  infer  the  extreme  ra- 
riety  of  a  perfectly  homogeneous  crystalline  lens.  To  my 
right  eye  a  distant  street  lamp  has  the  appearance  shown  in 
Fig.  49.  On  comparing  this  with  the  spectrum  of  the  lens 
(Fig.  48)  it  will  be  seen  how  nearly  they  agree.  There  are 
eight  rays  to  the  star,  and  clear  indications  of  eight  sectors  to 
the  lens,  and  the  directions  of  the  rays  coincide  perfectly  with 
the  positions  of  the  sectors. 

.  §  208.  Another  manifestation  of  this  irregular  astigmatism  of 
the  lens  is  polyopia  monocularis,  though  it  is  seldom  present 
as  a  normal  condition  sufficiently  marked  to  attract  atten- 
tion. It  can  be  experimentally  demonstrated  in  the  following 
manner :  Take  a  small  black  dot  on  a  white  ground,  or  better 
still,  a  small  white  point  on  a  black  ground,  such  as  can  be  ob- 


POLYOPIA    MONOCULARIS    IN    IRREGULAR   ASTIGMATISM.        l8l 

tained  by  scraping  the  enamel  from  a  visiting  card  on  a  piece 
of  black  velvet,  and  arming  the  eye  with  a  strong  convex  lens 
(6  or  8  D)  in  order  to  render  it  myopic  and  avoid  the  contrac- 
tion of  the  pupil  associated  with  accommodation,  bring  it  close 
to  one  of  the  small  white  scales  having  a  diameter  of  about 
l/3  mm.  When  the  bright  spot  is  brought  very  close  to  the 
eye  and  passes  within  the  point  of  distinct  vision,  it  does  not 
become  a  broad  even  circle  of  diffusion,  as  it  would  do  were 
the  crystalline  lens  perfectly  homogenous,  but  breaks  into  a 
series  of  grayish  figures  around  a  darker  center.  Each  one 
of  these  figures  is  the  image  of  the  bright  spot  formed  by  its 
corresponding  lens  sector.  Fig.  50,  which  is  borrowed  from 
Helmholtz,  shows  the  polyopia  produced  by  the  lens  in  the 
right  (a)  and  left  (b)  eye  of  that  great  scientist. 

fig-  50- 


POLYOPIA  MONOCULARIS  (HELMHOLTZ). 

In  neither  of  my  own  eyes  is  the  polyopia  so  marked  as 
that  represented  in  these  figures,  from  which  I  judge  that  my 
lenses,  though  far  from  homogeneous,  are  yet  more  free  from 
inequalities  of  refraction  than  is  usual.  Each  one  of  these 
images  shows,  likewise,  fringes  of  colors,  demonstrating  the  ex- 
istence of  a  chromatic  aberration  as  well.  I  find  this  chromatic 
phenomenon  quite  marked  in  my  own  eyes. 

§  209.  Monocular  polyopia  is  one  of  the  most  marked 
features  of  abnormal  irregular  astigmatism  of  the  lens,  and  is 
most  frequently  found  associated  with  incipient  senile  cataract. 
The  sclerosing  process  in  the  lens  does  not  commonly  affect 
the  different  sectors  equally,  and  the  result  is  such  a  difference 


1 82  OTHER    CAUSES    OF    IRREGULAR    ASTIGMATISM. 

in  their  refraction  as  leads  to  two  or  more  images  of  the  same 
object.  Sometimes  the  first  indication  of  the  formation  of  cat- 
aract is  the  appearance  of  two  or  more  horns  to  the  moon  and 
multiple  images  of  a  distant  street  lamp. 

§  210.  Dislocation  of  the  lens,  in  addition  to  producing  in 
certain  instances  a  regular  astigmatism,  gives  rise  also  to  the 
irregular  form,  and  a  certain  part,  probably,  of  the  normal  ir- 
regular variety  comes  from  a  want  of  centering  of  the  cornea 
and  lens.  Injuries  to  the  capsule  and  zonula  which  allow  the 
lens  to  become  irregularly  curved  will  also  have  the  same 
effect. 

§  211.  Mauthner  is  of  the  opinion  that  the  lenticular  variety 
of  irregular  astigmatism  is  increased  on  accommodation  for 
near  objects.  He  accounts  for  this  by  supposing  that  the  cap- 
sule on  relaxation  of  the  zonula  falls  into  folds  which  would,  of 
course,  mar  the  uniformity  of  the  lens  surface  and  lead  to  ir- 
regular refraction.  This  wrinkling  of  the  capsule  he  claims  to 
have  demonstrated  as  an  actuality. 

§  212.  If  we  make  exclusion  of  the  monochromatic  oberra- 
tion  in  the  principal  meridians  demonstrated  by  Prof.  Hark- 
ness,  (§  29)  and  that  demonstrated  by  myself  (§  14)  neither 
of  which  are  correctible  by  cylinders,  there  is  no  corneal  astig- 
matism of  the  irregular  form  which  we  can  consider  as  normal. 

And  while,  as  we  have  seen,  in  the  majority  of  instances 
lenticular  astigmatism  is  congenital,  with  few  exceptions  irreg- 
ular corneal  astigmatism  is  acquired.  We  meet,  however, 
sometimes  with  a  class  of  cases  (and  they  are  getting  more 
numerous  since  we  have  now  at  command  the  proper  means  in 
keratoscopy  for  their  easy  detection)  in  which  there  are  ine- 
qualities on  the  surface  of  the  cornea  that  is  still  transparent, 
and  where  there  is  no  history  of  a  past  inflammatory  affection. 
In  such  cases  there  was,  in  all  probability,  an  ulceration  of  the 
cornea  during  intra-uterine  life. 

It  would  appear  from  this  that  the  formative  processes  in  the 
cornea  are  much  more  regular  and  constant  than  those  of  the 
lens. 

§  213.  The  most  common  causes  of  irregular  astigmatism  in 


DIAGNOSIS    OF    IRREGULAR    ASTIGMATISM.  183 

the  cornea  are  inflammations  and  injuries  of  its  substance.  The 
reparative  processes  following  these  pathological  conditions 
are  seldom  so  perfect  as  to  leave  the  curvature  or  homogeneity 
unaltered  ;  and  even  a  slight  change  in  either  of  these  particu- 
lars will  be  sufficient  to  affect  in  an  appreciable  manner  the 
distinctness  of  the  retinal  inage.  The  amblyopia  under  such 
conditions  does  not  depend  solely  on  the  opacity  due  to  the 
effusion  and  organization  of  inflammatory  material  in  the  cor- 
neal  substance,  but  results  mainly  from  the  distortion  and 
blurring  of  the  image  caused  by  the  irregular  dispersion  of  the 
light  rays,  and  this  distortion  and  indistinctness  of  the  image 
are  quite  as  marked  when  the  defect  is  unattended  with  any 
opacity,  as,  for  example,  in  resorption  ulcers  with  clear  bot- 
toms and  edges.  The  condition  of  vision  in  these  astigmatics 
is  very  well  imitated  by  looking  through  a  pane  of  very  bad 
window  glass  which  has  irregular  surfaces  and  inequalities  in 
its  substance. 

§  214.  DIAGNOSIS  OF  IRREGULAR  ASTIGMATISM. — Abnormal 
irregular  astigmatism  of  the  lens  is  readily  determined  in  the 
following  manner  :  The  patient  is  caused  to  look  with  each 
eye  separately  at  a  small  distant  point  of  light,  such  as  Bonders 
used  in  his  original  method  for  determining  regular  astigma- 
tism (§  80),  and  if  it  does  not  appear  single,  but  on  the  con- 
trary, broken  up  into  two  or  more  spots,  the  diagnosis  of  ir- 
regular astigmatism  is  fixed ;  and  if  on  further  examination  the 
cornea  is  found  to  be  regular  in  curvature,  its  seat  in  the  lens 
is  placed  beyond  doubt. 

This  kind  of  astigmatism  being  most  commonly  met  with 
in  commencing  cataract,  the  opacities  of  the  lens  associated 
with  the  change  in  the  sectorial  refraction  can  be  seen  by  the 
oblique  method  of  illumination  or  by  simple  illumination  with 
the  ophthalmoscopic  mirror ;  in  the  latter  case  revealing  them- 
selves as  dark  or  black  lines  or  spots  against  the  red  back- 
ground of  the  fundus. 

§  215.  If  there  be  a  dislocation  of  the  lens  leaving  its  edge 
in  the  area  of  the  pupil,  the  margin  will  be  seen  as  a  bright 
curved  line  on  oblique  illumination  and  as  a  curved  black  line 


184    KERATOSCOPE    IN  DIAGNOSIS  OF  IRREGULAR    ASTIGMATISM. 

on  direct  observation  of  the  fundus  by  the  mirror  alone.  The 
bright  line  in  the  first  instance  is  due  to  the  reflection  of  the 
incident  light  from  the  edge  of  the  lens,  having,  of  course  the 
color  of  the  light  used,  being  yellow  if  it  is  artificial  and  white 
if  day  light. 

The  black  line  in  the  other  method  conies  from  a  total  reflec- 
tion of  the  light  coming  from  the  illuminated  fundus  along  the 
edge  of  the  lens,  leaving  a  narrow  unilluminated  space  in 
striking  contrast  to  the  otherwise  brilliantly  lighted  background. 
It  often  happens  that  two  images  of  the  fundus  visible  at  the 
same  time  can  be  obtained  in  the  indirect  method  of 
ophthalmoscopic  examination,  one  through  the  lens  and  one 
through  the  pupillary  space  which  is  free  of  the  lens. 

§  216.  Irregular  corneal  astigmatism  is  most  easily  diagnosed 

Fig-  5i- 


o 

p 


KERATOSCOPIC  APPEARANCE  OF  THE  CORNEA  w  A  CENTRAL  CORNEAL  OPACITY. 

by  keratoscopy,  and  best  by  means  of  the  disk  of  Placido  de- 
scribed in  §  156.  Wecker's  square  (  §  158)  can  also  be  used, 
but  it  is  much  inferior  to  the  concentric  circles.  In  making 
the  examination,  the  patient  is  seated  with  the  back  to  a  win- 
dow and  the  figures  are  so  held  as  to  get  a  good  reflection  of 
them  from  the  corneal  surface.  Any  irregularity  of  curvature 
is  then  at  once  manifest  in  a  distortion  or  unequal  thickness  of 
one  or  more  of  the  circles,  or  a  distorted  form  of  the  square. 
The  shapes  which  they  assume  are  sometimes  quite  fantastic. 
They  will  be  best  illustrated  by  the  actual  appearances  in 
some  cases  selected  from  my  case-book. 

Figure  51  represents  in  A  the  appearance  of  Placido's    disk, 


KERATOSCOPIC    APPEARANCES  IN   IRREGULAR  ASTIGMATISM.    185 

and  in  B  that  of  Wecker's  square,  as  they  were  reflected  from  a 
cornea  having  an  opacity  near  its  center,  the  result  of  an  ulcer. 
It  will  be  observed  that  in  this  case  there  is  also  some  regular 
astigmatism  as  shown  by  the  drawing  out  of  the  circles  and 
square  from  above  inward  downward  and  outward,a  not  unusual 
consequence  of  corneal  ulceration. 

Fig.  52. 


KERATOSCOPIC  APPEARANCE  IN  A  SMALL  CORNEAL  INFILTRATION. 

Figure  52  shows  the  reflection  from  a  cornea  in  which  there 
was  a  small  circumscribed  opacity  resulting  from  an  infiltra- 
tion, the  rest  of  the  cornea  being  clear.  V  could  not  be 
brought  to  more  than  4/60  even  after  a  correction  of  the  myopia 
that  was  present. 


53- 


§217.  Should  neither  Placido's  disk  or  Wecker's  square  be  at 
command,  the  reflection  of  a  window  sash  with  its  rectangular 
figures  will  show  any  irregularities  that  may  be  on  the  corneal 
surface.  In  this  examination,  of  course,  the  patient  must  sit 
facing  the  window. 


1 86  EXAMINATION  BY    OBLIQUE    ILLUMINATION. 

§  2 1 8.  The  reflection  figures  in  any  one  of  these  methods  of 
keratoscopy  are  not  the  same  from  all  parts  of  the  cornea.  The 
changes  in  form  as  the  eye  is  moved  in  different  directions, 
while  the  object  is  stationary,  are  quite  kaleidoscopic  in  their 
character.  Fig.  53  gives  two  forms  of  Placido's  disk  in  a  case 
of  cystoid  cicatrix  situated  at  the  upper  inner  sclero  corneal 
margin;  one,  A,  from  over  the  center  of  the  pupil,  showing  the 
extreme  flattening  of  the  cornea  in  the  direction  of  the  scar, 
and  the  other,  B,  when  the  eye  was  turned  IO°  inward. 

§  219.  Irregularities  of  the  corneal  surface,  even  where 
there  are  no  opacities,  can  often  be  detected  by  direct  inspec- 
tion, and  particularly  when  oblique  illumination  is  used.  The 
appearance  of  an  ulcer  with  a  clear  bottom,  for  instance,  is 
quite  characteristic  when  the  light  is  concentrated  on  it  by  a 
convex  lens.  The  edge  appears  as  a  bright  ring,  the  sides 
darker,  on  account  of  the  reflection  of  the  light  out  of  the  line 
of  the  observers'  vision,  and  the  center  as  a  bright  spot  of  light. 
The  same  appearances  will  be  found  also  in  a  transparent  cir- 
cumscribed elevation  of  the  surface.  These  ulcers  and  eleva- 
tions, whether  transparent  or  not,  cast  shadows  on  the  anterior 
face  of  the  iris.  In  the  case  of  a  transparent  elevation,  the 
shadow  will  have  a  bright  center  surrounded  by  a  dark  ring, 
while  in  the  case  of  a  depression  there  will  be  dark  center  with 
a  brighter  rim.  The  surface  of  the  iris  seen  through  these  ir- 
regularities often  presents  a  wavy  appearance  which  changes 
as  the  point  of  view  is  changed. 

§  220.  All  these  circumscribed  alterations  of  curvature  and 
opacities  reveal  themselves  as  dark  spots  on  a  red  back-ground 
when  the  fundus  is  illuminated  by  the  ophthalmoscopic  mirror, 
the  light  from  the  bottom  of  the  eye  being  either  reflected  or 
refracted  by  them  in  such  a  manner  that  little  or  none  of  it 
which  should  pass  through  them  reaches  the  eye  of  the  ob- 
server. 

§  221.  A  certain  and  often  a  considerable  amount  of  irregu- 
lar astigmatism  of  the  cornea  is  manifest  during  the  healing  of 
the  wound  after  cataract  extraction,  and  particularly  when  it  is 
complicated  with  inflammation  either  of  the  cornea  itself  or 
of  the  anterior  portion  of  the  uveal  tract. 


IRREGULAR  ASTIGMATISM  AFTER  CATARACT  EXTRACTION.   187 

I  extracted  an  opaque  lens  from  the  R  eye  of  John  O'N by  means  of  Weck- 

er's  incision  and  an  iridectomy.  The  operation  was  perfectly  smooth  and  normal  and 
no  symptoms  of  irritation  showing  themselves  he  was  allowed  to  leave  the  hospital 
at  the  end  of  the  ninth  day.  Three  days  after,  he  presented  himself  again  with  a 
pronounced  iritis.  The  wound  which  at  the  time  of  his  discharge  appeared  well 
united  showed  signs  'of  separation,  and  the  lips  were  infiltrated  and  gray.  I  made 
measurements  with  the  keratometer  and  found  115°  r  =  10  mm.  10°  r  =  73/4  mm., 
a  difference  in  refraction  amounting  to  13  D. 


Fig-  54- 


KERATOSCOPIC  IMAGE  AFTER  CATARACT  EXTRACTION. 

A  keratoscopic  examination  with  the  disk  of  Placido  showed  an  amount  of  wrink- 
ling ot  the  cornea  as  exhibited  in  Fig.  54.  The  iritic  inflammation  was  most  per- 
sistent, and  it  was  six  weeks  before  there  was  any  evidence  of  abatement.  He  was 
examined  with  the  keratoscope  and  keratometer  from  time  to  time  and  there  was  no 
alteration  observed  until  the  inflammation  began  to  subside.  But  ev»n  when  ihere 
was  no  longer  any  inflammation  going  on,  there  was  quite  an  irregularity  in  the 
course  of  the  rings,  and  it  was  only  after  I  had  made  a  discision  of  the  secondary 
cataract  that  the  figure  became  regularly  oval.  This  case  shows  quite  conclusively 
that  the  contraction  of  the  capsule  especially  when  accompanied  with  inflammatory 
deposits  is  capable  of  drawing  on  the  base  <5f  the  cornea  in  such  a  manner  as 
to  wrinkle  its  surface. 

§  222.  The  operation  of  iridencleisis — now  seldom  performed 
— the  operation  for  iridectomy,  and,  in  fact,  any  traumatic  in- 
jury to  the  cornea,  or  sclero-corneal  margin  is  liable  to  be 
followed  by  a  greater  or  less  amount  of  irregularity  in  curva- 
ture which  will  mar  the  distinctness  of  the  retinal  image.  In 
all  cases  of  injury  to  the  anterior  portion  of  the  eye  where  re- 
duced visual  acuteness  follows,  a  keratoscopic  examination 
should  be  made  to  determine  how  far  irregularity  in  corneal 
curvature  is  the  cause. 

§  223.  Changes  in   the  tension  of    the   eye-ball — hypo-and 


188  SYMPTOMS    OF    IRREGULAR    ASTIGMATISM. 

hypertony  —  often  affect  very  markedly  the  character  of  the 
corneal  curvature.  The  evenness  of  the  corneal  surface  is  not 
often  affected  by  an  increased  tension,  but  where  the  tension 
is  reduced  some  irregularity  is  seldom  absent.  Fig.  55  shows 
the  reflection  image  of  the  disk  from  the  left  eye  of  Mrs.  C., 
which  was  affected  with  ophthalmo-malacia  in  consequence 
of  a  chronic  uveitis  following  a  dislocation  of  the  lens.  The 
ball  was  much  smaller  than  the  other,  and  the  tension  was  re- 
duced to  —  3. 


55- 


KERATOSCOPIC  IMAGE  IN  OPHTHALMO-MALACIA. 

§  224.  The  symptoms  of  irregular  corneal  astigmatism  are  es- 
sentially the  same  as  those  found  in  the  same  form  of  lenticu- 
lar astigmatism.  These  are  :  a  dazzling  sensation  which  comes 
from  the  diffusion  of  light  .over  the  retina  caused  by  the  dis- 
persion of  the  light  rays  by  the  semi-opaque  spots,  depressions, 
elevations  and  irregularities  of  curvature ;  diplopia  or  polyopia 
arising  from  the  different  images  formed  by  the  different  parts 
of  the  same  refractive  surface  ;  distortion  of  the  outlines  of  ob- 
jects from  an  unequal  refraction  in  the  same  plane — making  a 
straight  line,  for  example  to  appear  crooked ;  amblyopia  from 
the  indistinctness  of  the  principal  retinal  image  due  to  the 
causes  just  stated  ;  and  frequently  an  asthenopia,  the  expres- 
sion of  muscular  strain  from  the  necessity  of  holding  work 
close  to  the  eyes  or  of  mental  fatigue  in  attempting  to  obtain 
definite  sensations  from  indistinct  impressions. 

§  225.     The  regular  form  of  astigmatism  which  is  frequently 


TREATMENT    OF    IRREGULAR    ASTIGMATISM.  189 

found  associated  with  these  corneal  changes  must  be  treated 
in  the  manner  described  in  the  chapter  devoted  to  that  subject. 

§  226.  In  the  treatment  of  the  irregular  form  the  indications 
are  to  cause  the  light  to  pass  through  the  most  regularly 
curved  part  of  the  cornea  and  to  cut  off  that  which  passes 
through  the  portion  which  only  serves,  by  its  diffusion,  to  ren- 
der the  image  indistinct. 

§  227.  One  way  of  accomplishing  this  is  to  place  a  small 
hole  or  a  narrow  slit,  I  to  2  mm.  wide,  in  an  opaque  disk  such 
as  Bonders  used  in  his  first  investigation  of  regular  astigma- 
tism, opposite  the  most  evenly  refracting  portion  of  the  cor- 
neal surface.  By  this  means  all  rays  are  cut  off  except  those 
going  through  the  part  corresponding  to  the  slit,  and  this  then 
represents  practically  the  refracting  surface  of  the  cornea.  We 
can  then  proceed  to  examine  this  part  of  the  refracting  media 
of  the  eye  in  the  same  way  as  when  the  whole  cornea  is  ex- 
posed, and  determine  the  character  and  degree  ofitsametropia 
should  any  be  present. 

In  some  cases  we  find  a  very  considerable  augmentation  of 
visual  power,  particularly  for  near  objects  by  this  means,  but 
it  is  not  so  applicable  to  distant  vision  on  account  of  the  nar- 
rowing of  the  visual  field.  And  as  a  matter  of  my  experience, 
the  improvement,  after  the  correction  of  whatever  ametropia 
(including  regular  astigmatism)  that  may  be  found  on  a  careful 
examination,  that  is  produced  by  the  addition  of  the  stenopaic 
apparatus,  is  not  sufficient  to  justify  its  employment  except  in 
rare  cases. 

§  228.  Another  method  is  to  remove  the  pupil,  either  by 
making  an  iridectomy  or  by  the  operation  of  iridencleisis,to  such 
a  position  that  it  shall  lie  behind  the  most  regularly  curved 
portion  of  the  cornea. 

It  frequently  happens  that  there  is  a  central  opacity  of  the 
cornea  which  covers  the  pupillary  area,  and  we  have  a  choice 
of  several  positions  at  which  to  make  the  artificial  pupil.  We 
should,  of  course,  under  such  circumstances,  choose  that  place 
where  there  is  least  irregularity  of  corneal  curvature.  This 
we  are  enabled  to  do  by  means  of  the  concentric  circles  or  the 


KERATOCONUS. 

square.  We  get  reflections  successively  from  the  various  parts 
of  the  surface  until  one  part  is  found  which  offers  least  irregu- 
larity of  outline  and  make  the  pupil  to  lie  under  that.  Such 
iridectomies — as  should  all  iridectomies  made  for  visual  pur- 
poses— must  be  small. 

§  229.  KERATOCONUS.  The  cornea,  as  a  result  of  inflamma- 
tory changes  in  its  substance  may  become  very  much  dis- 
tended in  all  directions  and  assume  somewhat  the  shape  of  a 
globe  (kerato-globus) ;  or  it  may  become  bulged  out  at  a  cer- 
tain locality  (keratectasia) ;  or  it  may  assume  the  form  approx- 
imating that  of  a  cone  (keratoconus).  All  of  these  conditions 
will  give  rise,  of  course,  to  the  phenomena  of  irregular  astig- 
matism. These  consequences  of  inflammation  are  most  com- 
monly associated  with  opacities  which  still  further  mar  the  dis- 
tinctness of  the  retinal  images. 

But  there  is  one  form  of  keratoconus  which  is  developed  in 
a  clear  cornea  without  any  changes  in  the  transparency  of  the 
tissue.  It  was  known  among  the  earlier  writers  as  "  staphy- 
loma  pellucida."  There  are  some  reported  cases  in  which  the 
change  was  probably  congenital,  but  for  the  most  part  it  is  one 
of  gradual  development. 

§  230.  The  precise  nature  of  these  changes  and  the  pathology 
lying  at  the  root  of  them  have  not  been  definitely  settled,  but 
there  is  scarcely  any  doubt  that  the  tissue  of  the  cornea  is 
thinned  at  its  apex  and  thickened  at  its  base,  and  that  it  is  not 
the  result  of  an  inflammation  of  the  substance  of  the  cornea — 
at  least  in  the  ordinary  acceptance  of  the  term  inflammation. 
It  usually  commences  about  the  fifteenth  year  and  stops  about 
the  twenty-fifth,  though  it  is  not  always  progressive  during 
that  period.  It  occurs  with  much  greater  frequency  in  women 
than  in  men. 

|  231.  The  first  of  the  more  modern  writers  to  describe  this  condition  was  Scarpa, 
in  his  treatise  published  in  1802.  As  a  matter  of  historic  interest  I  quote  the  case  re- 
corded by  him.1 


1  From  the  French  edition  translated  from  the  Italian  by  Foumier-Pescay   and  Be- 
gin.   Paris.     1821.    Tome  2.     P.  214. 


FIRST    DESCRIPTION    OF    KERATOCOMUS.  19! 

"Not  long  ago  it  happened  to  me  to  observe  a  peculiar  affection  of  the  cornea, 
which  I  am  not  able  to  classify  unless  it  be  under  the  heading  of  staphyloma.  In  a 
woman  35  years  of  age,  with  naturally  prominent  eyes,  the  centers  of  the  two  cornese 
were  protruded  without  any  apparent  cause,  in  such  a  manner  that  this  membrane  no 
longer  formed  the  segment  of  a  regular  sphere  affixed  by  its  base  to  the  sclerotic,  but 
assum  ed  exactly  the  shape  of  a  pointed  cone.  Viewed  laterally  the  cornea  had  the 
appearance  of  a  small  transparent  funnel  applied  by  its  base  to  the  sclerotic.  During 
some  movements  of  the  globe  the  point  of  the  cone  seemed  somewhat  less  transpar- 
ent than  the  base ;  in  other  movements  this  effect  was  not  apparent.  Yet  at  the 
places  where  this  transparency  was  least,  there  was  sufficient  to  oppose  a  remarkable 
obstacle  to  vision.  On  placing  the  eye  directly  in  front  of  a  window  the  apex  of  the 
cone  reflected  the  light  to  such  an  extent  that  it  appeared  as  a  brilliant  point ;  and  as 
this  occurred  directly  in  front  of  the  pupil,  already  contracted,  the  woman  could  only 
see  distinctly  in  a  subdued  light  which  allowed  the  pupil  to  dilate  sufficiently;  when 
the  light  was  strong  she  could  see  only  a  little,  and  confusedly." 

It  appears,  however  that  Beer1  had  noticed  some  condition  similar  to  this,  for  he 
says. 

"There  is  a  kind  of  staphyloma  worthy  of  remark,  which  I  have  seen  in  more  than 
one  case  of  hydrophthalmia.  The  cornea  in  such  cases  is  inconceivably  distended, 
but  it  does  not  lose  its  transparency.  The  patients,  notwithstanding  the  transpar- 
ency of  the  cornea,  saw  little  or  none  at  all." 

The  conical  character  of  such  a  cornea  seems  to  have  escaped  his  notice. 
Among  the  older  writers  mention   is  made   of  the  "pellucid   cornea"  by  St.  Yves 
(1722),  Manchart  (1748),  Taylor  (1750),  who  gave  it  the  name  "Ochlodes;"  Himly 
(1819),  who  gave  it  the  name  of  "Keratosis,"  and  v.  Ammon  (1831)   who   called  it 
"Keratoconus.'2 

The  first  thorough  examination  of  the  optical  phenomena  presented  by  the  coni- 
cal cornea,  I  find  in  Wardrop.1 

The  examination  was  made  by  Dr.  (afterwards  Sir  David)  Brewster,  and  I  add  his 
account  of  it  in  full  as  given  in  a  letter  to  Mr.  Wardrop,  (p.  119-20).  It  is  interesting 
among  other  things  from  the  fact  that  it  is,  perhaps,  the  first  attempt  at  the  em- 
ployment of  keratoscopy  in  the  diagnosis  of  abnormal  curvature  of  the  cornea. 

"When  you  first  mentioned  to  me  the  case  of  Miss ,     I  was  much  surprised  at 

the  number  of  images  which  she  observed  round  luminous  objects.  As  this  multipli- 
cation of  images  could  arise  only  from  some  irregularity  in  the  cornea  or  crystalline 
lens  which  gave  their  surface  the  form  of  a  polyhedron,  it  was  completely  inexplica- 
ble from  the  shape  of  the  cornea  itself  which  your  drawing  represented  (Fig.  56)  as  a 
regular  surface,  resembling  very  much  that  of  a  hyperboloid ;  for  the  only  indistinct- 
ness occasioned  by  a  cornea  of  this  kind  would  arise  from  the  concentration  of  the 
rays  before  they  fell  upon  the  retina. 

When  I  had  the  pleasure  of  examining  the  eye  itself,  the  difficulty  of  explanation 
was  in  no  respect  diminished.  In  every  aspect  in  which  the  cornea  could  be  viewed 
its  section  appeared  to  be  a  regular  curve,  increasing  incurvature  toward  the  vertex  . 
a  form  which  could  produce  no  derangement  in  the  refraction  ^of  the  incident  rays. 

1  Prakt  Beobactungen  ii.  d.  grauen  Starr  u.  d  Krankheit.  d.  Hornhaut.  Wien.  1791 

2  Essays  on  the  Morbid  Anatomy  of  the  Human  Eye.     Edinburgh.     1808. 


FIRST    ATTEMPT    AT    KERATOSCOPY. 

As  the  disease  was  evidently  seated  in  the  cornea,  which  projected  to  an  unnatw ' 
distance,  it  did  not  seem  probable  that  there  was  any  defect  in  the  structure  of  the 
crystalline  lens.  I  was  therefore  led  to  believe  that  the  broken  and  indistinct  images 
which  appeared  to  encircle  luminous  objects  arose  from  some  eminences  in  'he  cornea 
which  could  not  be  detected  by  a  lateral  view  of  the  eye,  but  which  might  be  rendered 
visible  by  the  changes  which  they  produced  upon  the  image  of  a  luminous  object 
that  was  made  to  traverse  the  surface  of  the  cornea.  I,  therefore,  held  a  candle  at 
the  distance  of  fifteen  inches  from  the  cornea,  and  keeping  my  eye  in  the  direction  of 
the  reflected  rays,  I  observed  the  variations  in  the  size  and  form  of  the  image  of  the 
candle.  The  reflected  image  regularly  decreased  when  it  passed  over  the  most  con- 
vex parts  of  the  cornea  ;  but  when  it  came  to  the  part  nearest  the  nose,  it  alternately 
expanded  and  contracted  and  suffered  such  derangements  as  to  indicate  the  presence 
of  a  number  of  spherical  eminences  and  depressions  which  sufficiently  accounted  for 
the  broken  and  multiple  images  of  luminous  objects." 


A  LATERAL  VIEW  OF  A  CONICAL  CORNEA.    (WARDROP). 

§  232.  The  diagnosis  of  this  condition  is  oftentimes  a  matter 
of  no  difficulty,  a  simple  inspection  of  the  cornea  in  profile  be- 
ing sufficient  to  show  the  conicity  quite  plainly.  There  is  also 
very  frequently  a  bright  reflex  at  the  corneal  apex  as  if  a 
tear  had  fastened  itself  there.  This,  however,  is  in  the 
higher  forms  of  the  anomaly.  In  the  lower  developments  these 
gross  changes  are  not  so  apparent,  and  we  must  then  resort  to 
other  methods  of  examination,  when  keratoconus  is  suspected. 

§  233.  For  this  purpose  there  is  nothing  better  than  a  careful 
and  systematic  examination  by  means  of  the  keratoscope.  In 
this  way  we  get,  through  the  changes  in  the  form  of  the  reflec- 
tion figures  at  various  localities,  a  very  good  idea  of  the  general 
form  of  the  surface,  as  well  as  of  the  changes  at  particular  por- 
tions. The  figures  are  small  at  the  apex  and  generally  in- 
crease in  size  as  they  approach  the  periphery.  It  occasionally 
happens  that  this  increase  is  very  regular,  showing  how  nearly 
perfect  the  cone  is.  The  following  is  an  illustration  of  this  : 


OPHTHALMOSCOPIC    CHANGES    IN    KERATOCONUS. 


193 


CASE  I.  It  is  the  case  of  Mrs.  R.  a  part  of  whose  history  relating  to  regular  as- 
tigmatism was  given  in  Chap.  XI,  \  175.  She  reports  that  up  to  her  sixteenth  year 
she  saw  well.  At  that  time  her  vision  began  to  fail  and  gradually  got  worse  till  her 
nineteenth  year,  since  which  time  it  has  remained  about  as  it  is  now.  On  October  6, 
1884,  the  time  of  my  first  examination,  V  =2-5/60.  With  —  6s  she  saw  with  either  eye 
No.  60  at  4  meters  ;  no  other  spherical  glasses  giving  further  improvement.  As  is  my 
habit,  I  then  made  an  ophthalmoscopic  examination  before  trying  cylindrical  glasses, 
since  I  often  obtain  thereby  important  indications  as  to  the  directions  of  the  meridi- 
ans, the  form  of  the  astigmatism,  etc.,  which  will  materially  shorten  the  examination 
and  add  to  its  accuracy. 


57- 


DISK  AND  LARGE  RETINAL  VESSELS  AS  SEEN  IN  KERATOCONUS,  WHEN  EXAMINED 
BY  THE  DIRECT  OPHTHALMOSCOPIC  METHOD. 


I  at  once  found  that  I  liad  to  do  with  a  case  of  keratoconus.  Even  in  the  inverted 
image  it  was  not  possible  to  see  all  parts  of  the  disk  clearly  at  once,  and  when  the 
auxiliary  lens  was  moved  from  side  to  side  there  was  that  paralactic  movement  of  the 
vessels  which  is  characteristic  of  keratoconus  when  this  method  of  examination  is 
used.  When  the  light  from  a  plane  mirror  was  thrown  into  the  eyes  from  a  distance, 
as  in  examination  by  skiascopy,  the  peculiar  unstable  shadow  crescent  of  conical 
cornea  was  beautifully  shown.  Examination  by  the  direct  method  was  in  the  high- 
est degree  unsatisfactory.  At  no  time  and  with  no  lens  was  it  possible  to  get  more 
than  a  small  portion  of  two  or  three  vessels  in  focus  at  once,  and  the  slightest  move- 
ment of  the  eye  of  the  patient  or  of  the  ophthalmoscopic  mirror  would  throw  these 
out  of  view  and  bring  others  forward.  Some  idea  of  the  peculiar  distortion  of  the 
vessels  may  be  obtained  from  Fig.  57,  which  represents  diagrammatically  the  disk  of 
the  R  eye  and  its  immediate  neighborhood  as  seen  with  a  +  4  behind  the  ophthal- 
moscopic mirror.  The  black  lines  represent  the  parts  of  the  vessels  seen  with  dis- 
tinctness, the  shaded  portions  the  parts  that  were  out  of  focus. 


194 


KERATOSCOPIC    APPEARANCES    IN    KERATQCONUS. 


The  radius  of  curvature  of  the  cornea  was  measured  by  the  keratometer  in  various 
meridians  and  in  different  parts  of  the  same  meridian.  The  most  nearly  regular  por- 
tion was  found,  not  directly  in  the  line  of  vision,  but  about  5°  outward  in  each  eye. 
At  this  place  in  L  180°  r  —  $«"*  (^/t  D),  90°  r  =  6mm  (34  D) ;  in  R  180°  r  = 
6s/«mm  (30  D),  90°  r  =  sVjmm  (36  D).  But  even  in  these  meridians  there  was  a 
great  change  in  the  figures  as  soon  as  the  place  of  measurement  was  removed  a  few 
degrees  from  this  point  The  shape  of  the  bands  became  very  much  distorted  and  it 
was  impossible  to  take  accurate  measurements.  It  was  apparent,  however,  that  the 
corneal  surface  became  flatter  as  it  approached  the  periphery.  This  distortion 
began  much  sooner  on  the  outer  side  in  both  eyes.  I  measured  in  L  the  meridian 


2)ou-n. 


KERATOSCOPIC  IMAGES  AT  VARIOUS  PARTS  OF  A  CONICAL  CORNEA. 

at  180°,  20°  inward  and  outward  from  the  apex,  and  found  r  inward  =  7.5mm,outward 
8mm.  The  distortion  was  also  greater  in  the  upper  than  in  the  lower  portion  of  the 
cornea.  An  examination  with  the  concentric  rings  revealed  an  approach  to  regularity 
of  curve  which  I  do  not  believe  is  commonly  met  with  in  keratoconus.  Fig.  58  shows 
the  form  of  Placido's  disk  at  the  center,  and  at  20°  upward,  downward,  inward  and 
outward.  It  will  be  seen  how  pear-shaped  it  becomes  when  reflected  from  the  sides 
of  the  cone,  indicating  a  gradual  flattening  towards  the  base.  The  similarity  in  the 
shape  of  the  four  lateral  reflections  shows  an  approximation  to  uniformity  in  curva- 
ture at  corresponding  distances  from  the  apex,  resembling,  somewhat,  an  ellipsoid  of 
revolution,  though  we  know  from  measurements  that  it  is  compressed  laterally.  The 
apex  itself,  however,  offers  a  very  considerable  amount  of  irregularity. 

§  234.  Such  regularity  is  quite   exceptional,  the  majority  of 
cases  being  more  like  the  following: 


KERATOSCOPIC    APPEARANCES    IN    KERATOCONUS. 


195 


CASE  II.  Miss  L.,  set.  19,  says  she  had  fairly  good  vision  up  to  three  years  ago. 
Since  that  time  it  has  gradually  deteriorated  until  now  she  can  barely  count  fingers 
at  3  meters.  In  Fig.  59  are  shown  enlarged  views  of  the  reflections  of  Placido's 
disk  from  the  corneal  apex  of  both  eyes.  The  image  became  larger  as  it  approached 
the  periphery  in  all  directions,  showing  an  increased  radius  of  curvature.  Not  having 
a  keratometer  at  command  at  that  time  no  measurements  of  radii  were  taken.  The 
reflection  figures  of  Wecker's  square  are  shown  below  those  of  the  circles  in  Fig.  59. 

59- 


KERATOSCOPIC  IMAGES  IN  CONICAL  CORNEA. 

The  irregularity  of  these  is  in  stril  jng  contrast  to  the  uniformity  of  the  disk  in  th 
case  of  keratoconus  just  described.  No  glasses  improved  distant  vision.  With  the 
unaided  eye  she  could  read,  L,  No.  5  of  Wecker's  scale,  and  R,  No.  7,  at  6  to  8 
inches.  When  a  diaphragm,  having  a  hole  I  mm.  in  diameter  was  placed  before  the 
eye,  she  could  read,  L  No.  I,  R,  No.  4,  of  the  same  scale  at  the  same  distance.  Dis- 
tant vision  was  not  materially  improved  through  this  stenopaic  hole. 

§  235.  There  are  other  methods  of  diagnosis,  which,  though 
less  accurate  than  keratoscopy,  are  nevertheless  of  value  and 
bring  out  very  characteristic  appearances. 

Among  these  the  ophthalmoscope  ranks  first.  When  light  is 
thrown  into  the  eye  with  the  mirror,  as  in  examination  by 
skiascopy,  the  center  of  the  pupillary  area  appears  bright, 
with  an  ill-defined  dark  ring  or  crescent  separating  it  from  the 
periphery, which  is  also  bright,  but  usually  less  so  than  the  cen- 
ter. This  dark  ring  or  cresent  is  not  fixed,  but  very  vacillat- 


196          OPHTHLMOSCOPIC    APPEARANCES    IN    KERATOCONUS. 

ing,  moving  with  each  change  in  the  position  of  the  eye  or 
mirror.  In  the  majority  of  cases,  when  the  mirror  is  at  a 
proper  distance  from  the  eye,  an  inverted  image  of  a  part  of  the 
fundus  can  be  seen  without  the  aid  of  an  auxiliary  lens, 
through  the  central  part  of  the  cornea.  This  image,  which 
may  often  not  be  more  than  a  portion  of  a  single  retinal  vessel, 
moves  in  the  same  direction  as  the  mirror  and  nearly  always 
changes  its  shape  with  a  change  of  its  position. 

All  these  phenomena  are  due  to  the  optic'al  properties  of  the 
corneal  cone.  The  central  part,  on  account  of  its  excessive 
curvature,  is  strongly  myopic  and  concentrates  the  rays  coming 
from  the  illuminated  fundus  at  its  far  pojnt  some  inches  in 
front  of  the  eye,  making  a  brilliantly  illuminated  area,  together 
with  an  inverted  image  of  the  objects  lying  in  that  part  of  the 
fundus.  Those  rays  which  fall  on  the  sides  of  the  cone  at  a 
certain  angle  suffer  total  reflection,  rendering  this  portion  of 
the  ophthalmoscopic  field  much  darker  in  comparison  with  the 
central  area.  Those  rays  falling  on  the  more  peripheral  and 
flatter  parts  of  the  cornea  pass  through,  but,  being  more  scat- 
tered than  the  central  ones  fewer  of  them  reach  the  eye  of  the 
observer;  hence  this  circumferential  portion  of  the  field  is  less 
brilliant  than  the  central. 

Examination  by  the  direct  ophthalmoscopic  method  fur- 
nishes equally  characteristic  phenomena.  It  is  impossible  to 
get  a  clear  and  distinct  view  of  all  the  parts  in  the  entire 
ophthalmoscopic  field  at  once.  A  vessel,  for  instance,  will  ap- 
pear with  sharply-defined  outlines  at  a  certain  part  and  then 
suddenly  become  blurred  and  thrown  out  of  its  course.  The 
outline  of  the  disk  is  not  distinct  in  all  its  parts,  and  the  ap- 
parent curvings  and  twistings  of  vessels  are  often  quite  fantas- 
tic ;  the  whole  presenting  an  appearance  which  might  easily  be 
mistaken  by  a  novice  for  a  pathological  condition. 

Fig.  57  is  intended  to  give  some  idea  of  how  the  fundus  ap- 
pears under  these  conditions.  The  most  marked  phenomenon, 
however,  in  connection  with  these  appearances  is  its  change- 
ableness.  The  slightest  movement  of  the  head  or  mirror 
throws  some  parts  clearly  in  view  out  of  the  focus,  and  brings 
others,  hitherto  obscure,  forwards. 


OPHTHAMOSCOPIC    APPEARANCES    IN    KERATOCONUS.          ip/ 

There  are  also  appearances  peculiar  to  this  form  of  irregular 
refraction  when  the  examination  is  made  by  the  indirect 
method.  Even  when  the  inverted  image  is  clear  and  distinct 
throughout,  there  are  differences  in  the  paralactic  movements  of 
the  different  parts  which  make  the  diagnosis  certain.  If  the 
refracting  media  are  symmetrical  in  their  refraction  as  a  whole, 
when  the  auxiliary  lens  is  moved  in  any  direction  perpendicu- 
lar to  the  line  of  vision,  the  image  moves  with  it  as  a  whole, 
because  all  parts  of  the  image  are  formed  on  the  same  plane ; 
but  if  there  is  such  irregularity  in  refraction  that  parts  of  the 
image  will  be  formed  in  several  different  planes,  movements  of 
the  lens  will  be  accompanied  by  unequal  movements  of  these 
separate  parts  of  the  image,  some  moving  much  more  rapidly 
than  others.  And  in  keratoconus  where  the  different  parts  of 
the  cornea  have  different  refractions  these  parallax  motions  are 
sometimes  very  striking. 

§  236.  The  subjective  symptoms  of  keratoconus  do  not 
differ  in  any  essential  particulars  from  those  of  the  other  forms 
of  irregular  astigmatism.  Vision  is  always  impaired,  and  dis- 
tant V  is  much  worse  in  comparison  than  near,  and  occasion- 
ally there  is  a  complaint  of  polyopia  monocularis.  Metamor- 
phopsia  or  a  distortion  of  images  is  also  a  not  infrequent  ac- 
companiment. 

§  237.  Treatment  of  Keratoconus. — Keratoconus  may  be 
treated  optically  or  by  operation. 

The  strictly  optical  treatment  has  not  until  quite  recently 
found  favor  with  the  profession. 

Bonders  gives  in  his  treatise  no  suggestion  of  glasses,  and 
the  only  mention  Mauthner  makes  of  them  is  to  express  an 
opinion  of  the  worthlessness  in  general  of  cylindrical  lenses  in 
this  class  of  cases. 

The  stenopalc  slit  or  hole  was  the  only  means,  other  than  op- 
erative, which  it  was  thought  worth  while  to  employ  for  the 
improvement  of  vision.  This  apparatus,  by  excluding  all  the 
rays  except  those  going  through  a  limited  portion  of  the  cor- 
nea cuts  off  a  large  amount  of  diffused  light  that  is  very  de- 
structive to  the  distinctness  of  the  retinal  image.  These  patients 


198  OPTICAL   TREATMENT    OF    KERATOCONUS. 

almost  universally,  by  instinct,  make  use  of  such  an  apparatus 
by  narrowing  the  palpebral  aperture.  It  is  not  always  a  matter 
of  indifference  over  what  part  of  the  cornea  the  slit  or  hole 
lies,  and  it  should  be  placed  successively  in  different  positions 
until  that  one  is  found  in  which  vision  is  clearest;  and  it  not 
infrequently  happens  that  the  addition  of  a  spherical  or  cylin- 
drical glass  contributes  still  further  to  the  distinctness  of  the 
image.  The  advantage  of  the  stenopaic  apparatus  is  confined 
almost  entirely  to  near  vision,  and  this  is  often  very  markedly 
improved.  It  is  seldom  usetul  for  distant  vision  on  account  of 
the  diminished  illumination  and  the  restriction  of  the  visual 
field. 

§  238.  But  a  great  improvement  in  vision  can  be  effected  in 
a  large  number  of  cases  by  means  of  spherical  or  cylindrical 
glasses  alone.  There  are  few  cases  in  which  there  is  not  a  greater 
or  less  amount  of  regular  astigmatism;  and  in  some  instances 
the  benefit  derived  from  a  correction  of  this  by  cylindrical 
glasses  is  very  great  as  shown  in  the  case  reported  in  §  175. 
The  chief  obstacle  that  has  hitherto  lain  in  the  way  of  a  more 
general  employment  of  cylinders  in  such  cases  is  doubtless  the 
great  difficulty  usually  experienced  in  unravelling  the  optical 
complexities  inherent  in  the  con  jition.  Few  surgeons  have 
the  time  or  patience  to  work  out  the  problem  with  lenses  and 
test  objects  alone  where  there  is  so  high  a  degree  of  amblyopia. 
The  ophthalmoscope  offers  little  or  no  assistance  in  the  task. 
It  is  here  that  keratometry  and  keratoscopy  find  one  of  the 
fields  for  their  most  satisfactory  application.  A  simple  inspec- 
tion of  the  corneal  reflection  of  the  concentric  rings  is  suffi- 
cient to  give  us  the  direction  of  the  principal  meridians,  and  if 
a  keratometer  is  at  hand,  it  is  easy  to  find  the  difference  in  the 
refraction  of  these  two  meridians,  expressed  in  dioptries,  data 
which  will  render  the  further  determination  of  the  refraction  of 
the  eye  comparatively  easy. 

§  239.  We  have  seen  in  §  1 86  et  seq  how  cylindrical  lenses 
fail  to  give  complete  correction  to  the  corneal  ellipsoid  in  reg- 
ular astigmatism.  It  is  apparent  that  they  will  be  much  less 
effective  in  correcting  the  paraboloid  curve  in  keratoconus. 


HYPERBOLIC  LENSES  IN  KERATOCONUS.          19  ) 

Such  a  surface  can  be  neutralized  only  by  a   lens   which  ap- 
proaches to  a  hyperbola  in  form. 

§  240.  Rahlmann,  of  Dorpat,  was  the  first  to  use  such  lenses 
for  the  correction  of  conical  cornea.  At  the  meeting  of  the  Hei- 
delbergCongress  of  Ophthalmologists  in  1879  he  exhibited  these 
lenses  for  the  first  time  with  the  report  of  a  case  in  which  they 
had  been  successfully  applied.  The  best  V  to  be  obtained  by 
concave  spherical  and  cylindrical  glasses  was  1/10  5  with  the 
hyperbolic  lenses  it  advanced  to  l/2.  Since  then  the  subject 
has  been  further  worked  up  by  Rahlmann  himself,  and  several 
others,  and  the  advantage  of  such  lenses  now  seems  estab- 
lished beyond  question.  All  cases,  however,  are  not  benefited 
in  the  same  degree,  and  some  are  not  benefited  at  all.  Up  to 
this  time  their  selection  has  been  somewhat  empirical,  but 
since  we  have  now  a  ready  means  for  measuring  the  corneal 
curvature  at  its  various  parts,  it  seems  possible  that  we  may  be 
able  to  determine  the  proper  correcting  lens  with  greater 
scientific  exactness.  The  principal  difficulty  at  first  will  be  in 
having  the  glasses  manufactured  with  the  curve  found  neces- 
sary by  the  measurements,  but  if  further  experience  demon- 
strates the  promising  usefulness  of  these  lenses,  optical  art  will, 
as  it  has  always  done,  keep  abreast  with  the  demands  made 
upon  it. 

Rahlmann  employs  two  series  of  hyperbolic  lenses,  which 
differ  from  each  other  in  the  length  of  the  hyperbola  axis. 
Series  "A  "  has  an  axis  of  lji  mm. .series  "B"  an  axis  of  2  mm. 
The  different  members  of  each  series  are  numbered  according 
to  the  size  of  the  assymptote  angle.  The  larger  this  angle  is 
the  less  the  surface  is  curved,  and  the  weaker  the  refracting 
power  and  vice  versa.  When  the  assymptote  cone  with  a  base 
of  30  mm.  has  a  height  of  I  mm.  (the  height  depending  on  the 
size  of  the  assymptote  angle)  it  is  No,  I  ;  when  it  has  a  length 
of  2  mm.,  with  a  smaller  assymptole  angle,  it  is  No.  2,  and  so 
on.  The  members  in  series  "  A "  having  a  shorter  axis  to 
begin  with  are  much  stronger  than  those  in  series  "  B  "  and 
are  more  pointed,  and  consequently  better  adapted  to  the 
sharper  corneal  cones.  Angelucci  has  foun,d  great  advan- 


2OO  OPERATIVE    TREATMENT    OF    KERATOCOUS. 

tage  from  a  combination  of  these  lenses  with  cylinders   in  the 
correction  of  keratoconus. 

§  241.  The  operative  treatment  of  keratoconus  is  of  two  kinds. 
One  has  for  its  object  a  change  in  the  shape  or  position  of 
the  pupil ;  the  other  aims  at  a  reduction  in  the  curvature  of 
the  cone. 

The  operations  on  the  pupil  consist  either  in  making  an 
iridectomy  (as  small  as  possible)  under  the  most  regularly  curved 
portion  of  the  cornea  or  in  removing  the  pupil  by  the  operation 
of  iridesis,  as  first  done  by  Critchett,  to  the  same  desirable  local- 
ity. This  last  operation  leaves  a  slit-like  pupil  which  offers 
the  same  advantages  as  a  stenopaic  apparatus.  Bowman  mod- 
ified it  by  making  the  operation  at  opposite  sides  (double 
iridesis)  causing  the  slit  to  extend  all  the  way  across  the 
width  of  the  iris.  This  is,  however,  a  questionable  improve- 
ment, and  is  probably  not  now  performed  by  any  one. 

§  242.  It  has  also  been  thought  by  some  that  the  performance 
of  an  iridectomy  has  stopped  the  progress  of  the  corneal 
change  during  the  period  of  its  development.  Others  have 
noted  an  arrest  of  the  process  under  the  local  use  of  atropine 
and  of  eserine. 

§  243.  The  treatment  of  the  cone  itself  is  addressed  to  a 
flattening  of  its  apex  and  a  reduction  of  its  curvature.  This 
is  accomplished  by  a  removal  of  the  top  of  the  cone  by  opera- 
tion and  the  subsequent  cicatrization  of  the  wound.  The  cic- 
atrization is  aided  sometimes  by  caustic  applications.  Special 
forms  of  trephine  have  been  been  devised  by  Bowman  and 
Wecker  to  remove  a  small  circular  piece  from  the  corneal 
apex.  For  the  manner  of  performing  these  operations  and  a 
description  of  the  special  instruments  used,  the  reader  must  be 
referred  to  the  chapter  on  operations  in  the  text-books  of 
ophthalmology  and  the  various  articles  on  the  subject  whose 
titles  are  to  be  found  in  the  appended  bibliography.  It  must 
be  said,  however,  in  regard  to  all  these  operative  procedures 
that  the  opening  of  the  anterior  chamber  to  such  an  extent,  is, 
at  least,  a  hazardous  undertaking,  involving  as  it  does  the  in- 
tegrity of  both  cornea  and  lens,  and  should  never  be  under- 
taken until  all  optical  means  have  failed. 


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NOTE  TO  SECTION  196— Pp.  170-171. 

Since  the  text  of  this  work  has  been  put  in  type,  I  have  made  a  series  of  experi- 
ments which  render  intelligible  some  of  the  peculiar  optical  properties  of  spherical 
lenses  when  held  obliquely  to  incident  pencils  of  light.  I  used  in  these  investiga- 
tions a  Snellen's  phakometer,  where  the  sources  of  the  pencils  are  seveial  small  holes 
near  the  periphery  and  at  Ihe  center  of  a  disk  2.5  cm.  in  diameter,  through  which 
light,  whose  rays  have  been  rendered  parallel,  passes.  The  lens  to  be  examined  is 
placed  in  the  path  of  these  rays,  and  turned  on  its  vertical  axis  and  its  focus  found 
by  means  of  the  image  of  these  holes  on  a  movable  screen,  for  various  degrees  of  in- 
clination. The  investigations  of  Pickering  and  Williams  have  already  shown  the  cyl- 
indrical action  thus  acquired  by  a  spherical  lens  (see  Table  II,  page  34),  but  their 
measurements  only  give  the  results  of  the  rays  passing  through  the  central  portion 
of  the  lens.  My  experiments  were  directed  to  finding  if  there  was  also  a  difference 
in  the  focus  of  the  rays  refracted  by  the  edge  of  the  lens  nearest  the  object  and  that 
corresponding  to  the  edge  farthest  removed  from  it.  This  I  found  to  be  the  case  and 
the  amount  of  the  difference  was  very  decided  for  even  medium  angles  of  inclina- 
tion. /  found  that  the  cylindrical  focal  plane  of  a  spherical  lens  placed  obliquely 
to  the  incident  pencils,  lies  obliquely  to  the  optical  axis,  aud  in  a  sense  contrary  to 
the  inclination  of  the  lens. 

In  Table  VII  are  given  the  foci  of  a  spherical  lens  of  +iD  for  every  5°  of  inclina- 
tion up  to  45°,  beyond  which  accurate  results  cannot  be  obtained  on  account  of  the 
general  diffusion  of  light.  In  the  second  column  is  given  the  increase  of  the  gen- 
eral spherical  refraction,  and  in  the  other  two  columns  the  foci  expressed  in  dioptrics 
and  decimals,  at  the  side  of  the  lens  nearest  the  object  (being  the  image  of  the  hole 
on  the  opposite  side)  (F)  and  at  the  side  farthest  from  it  (F1),  the  last,  of  course* 
being  the  image  of  the  hole  on  the  side  of  the  lens  nearest  the  object- 


NOTE. 

TABLE  VII. 


2O5 


Degrees  of  Inclina- 
tion. 

Spherical  Action. 

F. 

F.i 

5° 

o 

Slight. 

Slight. 

10° 

i.i 

i.  20 

1.25 

15° 

1.2 

1.30 

i-5 

20° 

1.25 

i-57 

i-75 

25 

1.30 

1-7 

2.2 

30 

1.4 

2.6 

3- 

40 

1.6 

3-6 

5-i 

45 

i-75 

5-2 

6.8 

I  also  experimented  with  other  lenses,  but  will  only  add  the  results  with  a  lens  of 
+8  D.,  giving  the  focus  at  the  center  of  the  lens(F°)  in  addition  to  the  two  at  the 
periphery. 


Degrees    of    In- 
clination. 

Spherical  Action. 

F. 

F°. 

/?». 

10° 

8.1 

8-3 

8.4 

8-5 

20° 

8.2 

8.7 

9- 

9-5 

30° 

8-5 

10. 

10.5 

"•3 

40° 

9- 

13-5 

15- 

17- 

The  superiority  of  obliquely  placed  spherical  to  the  ordinary  cylindrical  lenses,  in 
some  cases  of  cataract  extraclion,  is  probably  due  to  the  correction  of  a  difference  in 
the  refraction  in  the  different  parts  of  the  same  meridian,  (generally  the  vertical,  since 
the  incision  is  always  made  above  or  below)  by  this  len's  whose  refraction  gradually 
increases  from  one  extreme  of  a  corresponding  meredian  to  the  other.  In  other  words, 
it  corrects  a  certain  amount  of  irregular  astigmatism  resulting  from  the  corneal  wound. 

Keratometric  measurements,  in  these  cases  of  cataract  extraction,  at  various  points 
on  this  meridian  should  enable  us  to  measure  exactly  the  amount  and  character  of 
this  form  of  irregular  astigmatism  and  furnish  data  for  correction  of  the  defect,  either 
by  a  lens  inclined  to  a  certain  degree,  or  a  lens  ground  in  such  a  manner  as  to  give 
the  same  optical  effect. 

I  will  also  state,  in  this  connection,  that  I  found  the  same  results  as  to  character 
and  degree  when  a  cylinder  was  rotated  on  its  axis.  The  cylindrical  action  as  a 
whole  was  increased,  thus  confirming  the  views  of  Hay,  and  opposing  those  of  Sous 
(see  \  26,  pp.  34  and  35),  butt  here  was  also  the  same  inclination  of  the  focal  plane 
as  was  found  in  the  obliquely  placed  spherical  lens. 


APPENDIX. 


A  STATISTICAL  RECORD  OF  806  ASTIGMATIC  EYES. 


I  have  collected  in  the  following  table  the  data  furnished  by  475  cases  taken  in 
the  order  in  which  they  were  recorded  in  my  private  case-book  during  the  last  five 
years,  and  which,  I  hope,  may  be  of  some  value  to  the  future  student  of  astigmatism- 
These  475  persons  had  806  astigmatic  eyes,  showing  that  in  about  $\%  of  the  cases 
the  anomaly  was  unilateral. 

In  291  of  the  eyes  affected  with  all  degrees  of  astigmatism  the  visual  acuteness 
was  brought,  by  correction,  up  to  the  normal  standard  of  4/4»  being  about  36$.  This 
is  a  better  showing  than  that  alluded  to  on  page  168  where  in  2,000  cases  there  was 
normal  vision  in  only  10%.  This  computation  was  made  principally  from  Snellen's 
and  Van  Haaften's  statistics,  and  the  difference  between  the  two  is  probably  due  to 
the  fact  that  I  have  corrected  the  lower  degrees  more  frequently  than  they.  My 
clientele  is  drawn  largely  from  the  clerical  force  in  the  various  .departments  at  the 
National  Capital,  where  the  work  is  of  such  a  nature  as  to  cause  small  errors  in  re- 
fraction to  be  felt,  particularly  by  women. 

To  this  latter  fact  is  due  the  preponderence  of  women  in  my  tables,  there  being  276 
of  them  to  199  men. 

In  the  higher  forms  it  will  be  seen  on  a  consultation  of  the  tables  a  normal  visual 
acuteness  is  rarely  found.  In  504  of  the  806  eyes  the  principal  meridians  were  ver- 
tical and  horizontal. 

The  relative  frequency  of  the  various  forms  was  as  follows: 

Simple  myopic  astigmatism       -----  294  or  yj-%. 

Compound  myopic  astigmatism    -----  162  or  20.^.    . 

Simple  hypermetropic  astigmatism    -  210  or  26.%. 

Compound  hypermetropic  astigmatism          -        -        -  113  or  14.  %. 

Mixed  astigmatism    -        -        -        -        -        -        -  27  or    3-Jfc. 

Total  806      100. 

(206) 


APPENDIX.  2O7 

A  STATISTICAL  RECORD  OF  806  ASTIGMATIC  EYES. 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correcting  glasses  and  direction 
of  axis  of  cylinder. 

'^ision  after 
correction. 

I 

3.  F.  M. 

VI.,  40. 

L.-H/36  90°- 

R.+VS6  90°. 

20/20 
M/20 

2 

:.  M. 

M.,36- 

^.+0.5  90°. 
R.  +0.25  90°. 

% 

3 

R.  D.  D. 

M.-26. 

£-H/«  90°' 

;/s 

4 

V.  Me. 

F.,  17. 

L.—  1/30  1  80°. 
R.—  1/30  180°. 

4/6 

5 

A.  Me. 

F.,  38. 

L.—  1/30  180°. 

R.—  1/30  1  80°. 

4//6 

6 

H.  H.  H. 

F.,  20. 

L.  Em. 

R.—  1/40  1  80°. 

4/6 

7 

R.  M. 

M.,  23. 

L.  —  2.25  ;3  —  0.75  90°. 
R.  —  2.25  C;  —0-75  ^o0- 

4A 

8 

M.  S.  F. 

F.,40. 

L.—  1/40  1  80°. 

R.—  1/40  1  80°. 

V* 

9 

E.  T.  F. 

F.,  u. 

L.—  Vio  1  80°. 
R.—  1/10  180°. 

;/9 

10 

C.  M. 

M.,  38. 

L—  1/60  10°. 

R.—  i/eo  170°. 

% 

ii 

G.  K. 

M.,  24. 

L.+O.S  90°. 
R.+o.s  90°. 

J/4 

12 

S.  W.  B. 

M.,  26. 

L.—  0.75  1  80°. 
R.—  0.75  1  80°. 

J/4 

13 

E.  P. 

F.,  10. 

L.—  i  C—  0.25  180°. 
R.—  2  C  —o-5  1  80°. 

4/5 

14 

G.  R. 

F.,  42. 

L.+0.7S  140°. 
R.+i-S  20°. 

4/6 

15 

H.  M. 

F.,  14. 

L.  —  5  C  —  1-5  20°. 
R-—  5  C  —i-5  130°. 

4/6 
4/6 

16 

A.  C. 

F.,  21. 

L.+2.25  90°  C  —3-5  1  80°. 
R-+3-590°C—  1-75  180°. 

4/6 
4/6 

17 

H.  D.  B. 

M.,2;. 

L—  7  C—  r-75  r50- 
R.—  7C—  1-75  160°- 

4/6 
4/6 

18 

J.  L.  E. 

M.,3o. 

L.+2.5  90°. 
R.  Em. 

Vl2 

208 


STATISTICAL  RECORD. 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correcting  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

'9 

J.  W.  H. 

F.,49- 

L.+O.S  70°. 
R.  -t-o-s  120°. 

*/« 

V* 

20 

L.  G. 

F.,    12, 

L-+0-75  C  0.5  90°. 
R-+0-75  C  0.5  90°. 

V« 
V« 

21 

W.  L. 

M.,  14. 

L.+6  C  4-1.5  180°. 
R.+6C+i-5i8o°- 

4/5 

v« 

22 

L.B.  H. 

M.,  35- 

L.  —  a75  70°. 
R.  —  0.75  120°. 

4/« 

V* 

23 

0.  D.  W. 

M.,  25. 

L.+0.75  90°. 
R.-f-as  90°. 

*/4 

V* 

24 

M.  E. 

F.,24. 

L.40-5  90°. 
R.+0-5  90°- 

Vi 

V* 

25 

H.  H.  M. 

M.,34. 

L.+O.S  90°. 
R.+0.5  90°. 

4/4 
V* 

26 

L.E.  B. 

M.,  28. 

L.—  0.75  180°. 
R.—  0.5  180°. 

*/4 
V* 

2? 

E.W.  N. 

F.,39- 

L.  —  i  C  —  2  ^S0- 
R.+I  90°. 

4/4 
4/4 

28 

T.  A. 

F.,  45. 

L.  Em. 
R.+0.25  i8c°. 

*/• 

29 

H.  A.  H. 

F.,54. 

L.—  i  180°  C  +  2.5  90°. 
R-+I-5  C  +i  9°°- 

4/» 

4/6 

30 

I.  M.  C. 

F.,  22. 

L.+0-5  90°. 
R.-|-o.5  90°. 

4/4 
V*       • 

31 

A.  C. 

F.,  45- 

L.—  0.5  1  80°. 
K.—  0.5  1  80°. 

4/4 
4/4 

32 

T.  E.  M. 

M.,  25. 

L.—  0.5  C  —0.5  1  80°. 
R.  Amblyopic. 

4/4 

33 

A.  M.  M. 

M.,34. 

L.—  0.5  1  80°. 
R.—  0.5  180°. 

4/4 
4/4 

34 

B.  D. 

F.,20. 

L.  Amblyopic. 
R.—  6  180°. 

V. 

35 

S.  F.  T. 

M.,30. 

L.—  6  C  —i  1  80°. 
R.—  3  C  —i  140*. 

4/4 
4/» 

36 

T.  T. 

M.,  41. 

L.Em. 
R.—  i  1  80°. 

*/6 

37 

M.  G. 

F.,  18. 

L,—  8. 
R.—  SO—  i  »8o°. 

4/6 
4/6 

APPENDIX. 


2O9 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correcting  Glasses  and  direction 
of  axis  of  cvlinder. 

Vision     afli'- 
correction. 

\ 

38 

C.  E. 

M.,  46. 

L.  E. 
R.+0-75  1  80°. 

4/» 
'/• 

39 

A.  C. 

F.,  64 

M-i.75' 
R.+0.75  9,°. 

*/18 
4/!8 

4? 

j.  r.  A.. 

M.,  22. 

i-—  4  '^  —i-5  15°". 
R-—  5  C  —1-75  5°- 

'/« 

*/5 

4i 

C.  C.  N. 

F.,   36. 

L-f  2  C  +2  9°°- 

R.+0.75  S. 

V9 
4/9 

42 

O.  DeF. 

M.,  50. 

L.+0.75- 
R.+  I  C  +0.5  1  80°. 

4/5 
-"/» 

43 

E.  H. 

F.,  18. 

L.—  0.5  1  8°. 
R.—  0.5  180. 

V* 
*/« 

44 

J.R 

M.,  33. 

L.—  4  C  —i  1  80° 
R—5- 

V* 

4/* 

45 

J.  N.  P. 

M.,  46. 

L.—  0.5  90°. 
R.  Em. 

4/4 
'/« 

46 

C.  H.  B.. 

M.,  58. 

L-—  0-75  C  —0-75  95°- 
R.  —  0.5  C  —  °-5  9°°- 

4/5 
4/5 

47 

N.  G.  D. 

F.,  30. 

L.—  7  C  —i  90°- 
R.-3-5- 

.            4/18 
4/5           . 

48 

E.  H. 

M.,  50. 

L-—  3.5  C  —0-75  I8o°. 
R--3-5- 

<4/12 
4/12 

49 

S.  H.  P. 

M.,  35. 

L.—  8  ^  —i  180°. 
R.—  8C—  '-5  1  80°. 

4/18 
Vl6 

50 

M.  W. 

F.,  17. 

L.  —  2  C'—  °-5  l8o°- 
R.  —  2  C  —  0.5  70°. 

4/4 
4/4 

51 

E.  W. 

F.,  50. 

L.—  0.5  1  80°. 
R.—  0.5  1  80°. 

4/4 

4/4 

52 

C.  H.  W. 

M.,  21. 

L.  —  0.5. 
R-+I-5  C  +i  9°°- 

4/4 
Vl8 

53 

J.  A.  W. 

F.,  38. 

L.—  0.75  180°. 
R.—  0.5  1  80°. 

4/4 
4/4 

54 

J.  T.  W. 

M.,  40. 

L.—  1.5  20°  C  +2-75  IIO°- 
R.  Em. 

4/6 
4/6 

55 

H.  J.  H. 

F.,  36. 

L.+0-5  1  80°. 
R.+I-75- 

:;;. 

56 

E.  D. 

F.,  38- 

L.+0-75  90°  C  —0-75  l8o°- 
R-+0-75  90°  C—  °-75  180°. 

% 

210 


STATISTICAL    RECORD. 


Num- 
ber. 

Name. 

Sex  and  Age. 

Corteeting  Glasses  and  direction 
of  axis  of  cylinder. 

Vision     after 
correction. 

57 

W.  H. 

M.,  31- 

L.—7  C  —2  1  80°. 
R.-7C-I    1*0°. 

4ll 

58 

C.  H. 

F.,  28. 

L.+I  1  80°. 
k+i.25  10°. 

•/! 

59 

L.G.  B. 

F.,48. 

L.—  j  180°  0+0.7590°. 
R—  i   i.SoJ. 

4/s 

4/5 

60 

C  E. 

F.,40. 

L.-fas  90°  O  —  °-5  '80. 
R—  075  180^. 

;/* 

61 

M.  D. 

F.,  25. 

L.—  i  560°. 
R.—  1.5  120°. 

v! 

62 

M.  B. 

F.,  14- 

L.+0-5  14..°. 
R.+a5  140°. 

4/l 

63 

R.A.M. 

M..2& 

L.+I.25C+'  '80°. 
R.+2.5. 

4/5 
4/5 

* 

II.  \V.  B. 

M.,  31. 

L-+3-5C+'  90°. 
R.  Em. 

V. 

V« 

65 

CS.  E. 

M.,  36- 

L.—  2  1  80°  C  +0-75  90°. 

R.-2.5. 

% 

66 

E.B.J. 

F.,40. 

L.+0-5  90°  C  —0.5  180°. 
k.  •  0.5  90°. 

J/l 

67 

G.  H. 

M.,  u. 

i_—  0.75  180°. 
R.—  as  iSo°. 

*/; 

68 

J.  W.  H. 

F.,  35- 

k.—  a$  90°. 

4/5 

69 

C.S.B. 

M.,  36. 

L.+0-75  90°. 
R.+O-S  90°. 

:</: 

70 

M.C 

F.,  25. 

I-—  3  C  -2.580°. 
k.-7. 

*/! 

71 

\V.  II.  L. 

M.,  22. 

R.-o.7l  90°. 

)/4 

72 

T.J. 

M.,  49- 

L.—  as  90°. 
k.  Em. 

\\\ 

73 

B.J. 

F.,48. 

L-+I-5  C  +0.5  180°. 
R.  4-1.5. 

4/5 
4/5 

74 

C.A.B. 

M.,  2a 

L.—  9C—  2  1  80°. 
R.—  9  C  —2  1  80°. 

*/» 

75 

J.  A.C. 

M.,43- 

L.+0.75  180°. 
R,  Em. 

* 

APPENDIX. 


211 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correcting  Glasses  and  direction 
of  axis  of  cylinder. 

Vision     after 
correction. 

76 

D.  M. 

M.,  39. 

L.  —  0.75  125°. 
R.  Em. 

*/* 

77 

J.N. 

F.,  13- 

L.+i.  250+0.5  9°°- 
R+  1.  25  0+0.590°. 

4/5 
.    */5 

78 

M.  P.  B. 

M.,  22. 

L.+4  C  +3  5  90°. 
R.+6  90°. 

Vl8 

VM 

79 

J.  H. 

M.,  64. 

L.  —  2.5  C  —i  90°  • 
R.—  2.5  C  —  i  90°  • 

•|: 

80 

M.  J.  S. 

F.,  35.            !L.+2.5  C  +  1-25  60°. 
R.+2  5  C  +  J-25  "5°. 

% 

81 

A.  N. 

F.,  1  8. 

L—  4.5  C—  1-5  1  80°. 
R.-4-5- 

% 

82 

A.  H. 

M.,  42. 

L.+0.5  90°. 
R.+o-s  130°. 

V* 

4/4 

83 

M.  A. 

F.,  19. 

L.—  '/so  1  80°. 
R.  Em. 

2°/40 

84 

M.  H. 

F.,  13. 

L.-P/S6  90°. 

R.+  V-28  90°. 

2°/« 
20/« 

85 

S.  B. 

F.,  1  8. 

L.  +  VlO  C  +V30  90°- 
R.+VlO  C  +V30  90°. 

^/SO 
^/SO 

86 

M.  K. 

F.,  14. 

L.—  '/6   140°. 
R.—  '/6  20°. 

2°/30 
2°/30 

87 

W.  N. 

M.,  31. 

L.  +  l/16  C  +V»0  90°. 
R.  +  Vl6  C  +V30  90°- 

2°/20 

^/ao 

88 

M.  W. 

F.,  10. 

L.  (Staphyloma  of  cornea). 
R.—  Vso  80°  C  +V«o  170°- 

2°/20 

89 

A.  B. 

F.,  1  8. 

L.+V86  60°. 

R.—  »/«2  180°. 

2°/20 
2°/20 

90 

E.  S.  S. 

M.,  50. 

L.-V24- 

R.—  V*2  180°. 

2°/20 
2°/20. 

9i 

T.  M.  S. 

M.45- 

L.  +  '/36  I80°. 

R.+J/36  150°. 

2°/20     ' 

*v» 

92 

C.  M. 

F.,  30. 

L.—  1/40  1  80°. 

R.—  1/40  1  80°. 

2°/20 
2°/20 

93 

A.  P. 

F-,  33- 

L.+Vu  70°. 

R.-F/HllO°. 

2°/20 
^20 

94 

H.  H.  B. 

M.,  29. 

L.—  Vso  C  —  Veo  180°. 
R.—  Vso  C  —  Veo  1  80°. 

4/5 
4/5 

212 


STATISTICAL  RECORD. 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correcting  Glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

95 

M.  N. 

F.,  13- 

L.—  8C—  2-25  1  80°. 
R.—  8  C  —2.25  1  80°. 

v« 

v» 

96 

M.  G. 

F.,  20. 

L.+Vu  90°. 
R.+»/«  90°. 

*/4 

v« 

97 

A.  H.  M. 

M.,  19. 

L.+  Vtt  90°. 

R.+Vi«  90°. 

*/• 

V. 

98 

M.  W. 

F.,  22. 

L.—  2  180°. 
R.—  2  180°. 

•/• 

V. 

99 

A.H. 

F.,  45- 

L.+Vi«C+l/i690°. 
R.+VH- 

*/*4 
4/H 

100 

J.F. 

F.,  42- 

L.—  2.25  1  80°. 
R.—  2.25  1  80°. 

*/6 

*/5 

101 

E.C.  M. 

M.,  39. 

L.—  1.25  1  80°. 
R.—  1.25  180°. 

4/S 
4/5 

102 

M.  S.  T. 

F.,   20. 

L.—  »/«  180°. 

R.—  »/42  1  80°. 

4/« 
4/4 

103 

J.L. 

F.,   20. 

I  VnC—  V«i8o°. 
R.—  Vw  C  —  V«  180°. 

4/5 
4/5 

104 

O.J. 

M.,40. 

L.+V«  90°.- 
R.+V«  90°. 

4/4 
*/4 

105 

G.  L.P. 

F.,  30. 

L.—  Vso  1  80°. 
R.—  1/»  1  80°. 

4/5 
4/6 

1  06 

E.M. 

F.,  40. 

L.+V«i  90°. 
R.+V«  90°. 

V« 

V. 

107 

B.  H. 

F.,  15. 

L.—O.S  180°. 
R.—  0.5  1  80°. 

4/4 

4/4 

108 

J.  C.  D. 

M.,45- 

L.  Em. 
R.—  0.75.180°. 

V* 
V4 

109 

M.  W.  L. 

F.,  18. 

L.—  0.5  180°. 
R.—  as  1  80°. 

4/6 
4/5 

no 

F.  A.  P. 

F.,  19. 

L.—  i  ~  —  0.75  180°. 
R-  —  '75  C  —  0-75  'So0. 

*/» 
V» 

III 

L.P.  S. 

M.,  20. 

L.+0.5  90°. 
R.  —  0.75  1  80. 

4/4 
4/4 

112 

J.  B.  D. 

M.,32. 

L.—  0.25  1  80°. 
R.—  0.25  1  80°. 

4/4 
4/4 

"3 

G.  W.  P. 

F.,  31. 

L.—  aS  1  80°. 
R.—  0.5  180°. 

4/4 
4/4 

APPENDIX. 


213 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correcting  Glasses  and  direction 
of  axis  of  cylinder. 

Vision  'after 
correction. 

114 

H.  H.  Y. 

F.,  36. 

L.+  1.50  160  ^  —  0.75  20°. 
R.—  0.75  go0/ 

I 

"5 

C.  V.  R. 

M.,  40. 

L.-0.5  15°. 
R.—  0.5  90°. 

'','. 

116 

L.  B. 

F.,  1  8. 

L.  —  0.5  90°. 
R.  —  0.25  90°. 

4/4 

Vi 

117 

J.  G.  W. 

M.,  50. 

R.—  0.75  1  80°. 
L.—  0.75  1  80°. 

*/• 

*/5 

118 

J.  S. 

M.,  26. 

L.—  1.25  180°. 
R.+O-S  90°  C  —2.25  180°. 

4/4 
*/• 

119 

W.  B. 

M.,  29. 

L.+I.5  90°, 
R.Em. 

4/9 

1  20 

A.  D. 

F.,  50. 

L.-J-0-75  90°. 
R.+0.75  90°. 

*/6 
*/6 

121 

L.  M. 

M.,  24. 

L.—  1.5  1  80°  C  +0-75  90°. 
R.-i-S  i5°- 

v« 

V6 

122 

C.  W. 

M.,  ii. 

L.+O.S  20°. 
R.  Em. 

4/6 

123 

S.  E.  C. 

F.,  23. 

L.+0.5  100°. 
R.+0.25  90°. 

4/6 
4/6 

124 

M.  G. 

F.,  14- 

L.—  0.75  90°. 
R.+O-S. 

4/6 
4/5 

"5 

A.  J.  F. 

M.,  33- 

L.  —  0.5  90°. 
R.—  0.5  90°. 

I 

126 

M.  E.  T. 

F.,  22. 

L.+0.75  90°. 
R.+6.5  90°. 

•'<: 

127 

A.C. 

F.,  1  8.              L.—  i. 
R.—  4  C  —3  180°- 

4/9 
4/>8 

128 

S.  C. 

M.,  42.             L  —  3  C  —  l  9°°- 
R.—  4  C  —  °-5  90°  • 

*/9 
4/9 

129 

T.  W.  H. 

M.,  37.            L.+2.25ii5°. 
R.-J-0.75  120°. 

4/9 
*/9 

I30 

E.  S. 

M.,  61.             L.—  1.5  1  80°. 
R.  Em. 

4/8 
Vl2 

131 

F.  D. 

F.,  21.              R.—  0.5  1  80°. 
L.  Em. 

4/4 

I32 

A.  G. 

F.,  1  8.              I,.—  3C—  0-75  1  80°. 
R.  —  4. 

4/4 
4/4 

STATISTICAL  RECORD. 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correction  Glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

'33 

I.T. 

F.,  13. 

L.—  3O—o.75i8o°. 
R.—  3O—0-75  '80°. 

; 

'34 

M.  B. 

F.,8. 

L-+2-5  O  +2.25  90°. 
R.+2  O+2-5  90  . 

4/w 

'35 

J.S 

F.,  22. 

L.—  1.25  180°. 
R.—  3.5  180°. 

;/• 

136 

J.C. 

F.J* 

I-—  0.5  1  80°. 
R.—  0.75  180°. 

4/! 

137 

M.  P.  B. 

M.,  23. 

R-+4  O+3-5900. 
L-+4O+3-5900' 

•7- 

'38 

W.  M. 

M,2,. 

L.+3  O  +1.5  90°. 
R-+3  O  +i-5  90°. 

4/« 
v. 

'39 

P.O. 

M.,  18. 

L.—  1.25  180°. 
R.—  0.75  180" 

;/« 

140 

M  T. 

F.,40. 

L.—  loO—i-S  '80°. 

4/. 
4/w 

141 

M.  D. 

F.,  40. 

L+i90°. 
R+i.25  90°. 

;/4 

142 

T.  D. 

M.,5'- 

L.  —  10  O  —  '-5  20°. 
R—  ioO—  '  "0°. 

4/» 

J43 

A.  H. 

F,48. 

I-+o.75O+o.5'5o°. 
R-+0.75  O+0-5  40°. 

4/. 
4/. 

'44 

F.  H. 

M.,14. 

L,—  i.  5  40°  0^-2.75  120°+. 
R.—  i  1  80°  O+2-5  90°+. 

4/S 

'45 

A.  H.  F. 

M.,37- 

L.+0-5  140°. 
R.+05900. 

4/6* 

146 

J.S. 

F-.39- 

L.+O  5  90°. 
R.+0.5  90°. 

v! 

'47 

F.  E. 

M.,  1  6. 

L.-—  8  O—  '-75  '80°. 
R.—  8. 

4/'j 

148 

D.  W.  P. 

M.,38. 

L.—  4.53—0.540°. 
R.—  4-5  O—  '-5  '80°. 

4/5 
4/6 

149 

E.  P. 

F.,  13. 

L.  atrophy  of  o.n. 
R.—  0.75  180°. 

4/« 

'So 

L.F. 

F.,  16. 

L.-0.75450- 
R—  075'35°- 

V. 
*/• 

15' 

K.I. 

M.,  26. 

;  ()->  (amblyopia). 
R+  «  0+0.75  75°. 

V. 

APPENDIX. 


215 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

152 

T.  J.  M. 

VI.,  22. 

L.  —  0.75  1  80°. 
R,—  0.75  i  So0. 

v« 

•53 

R.  M. 

M.,23. 

L.  Fm 
R.-i  ,  .5  yo°- 

*/4 

'54 

E.  C. 

F.,  51. 

L.—  0.5  1  80°. 
R.—  0.5  180°. 

4/5 
V5 

'55 

G.  S.  P. 

M-,  45. 

L.+  I  75 
R.—  0.75  1  80°. 

v» 

4/« 

156 

R.  H. 

M.,    21. 

L.  —  2  C  —  1-5  90°. 
R.—  2  C  —2.  95°. 

4/4 
*/* 

'57 

W.  H.  P. 

M.,  28. 

L.-3C-;.55°;o 
R.—  2.5  C  —i  1  60  °. 

4/5 
4/5 

'58 

S.  P.  S. 

F.,  51- 

L.+0.75  135°. 
R.-f  0.75  45  , 

4/4 
4/5 

'59 

W.  C.  S. 

M.,  27. 

L.—  3  1  80°. 
R.—3  1  80°. 

4/6 
4/6 

160 

P.  C.  M. 

M.,29- 

L.+I. 
K.-f-O-S  90°. 

4A 

4/4 

161 

E.  S. 

M.,  27. 

I-—  4  C  —I   45°- 
K.  —  i  C  —  r   '^o. 

4/5 
V. 

162 

T.  B. 

M.,  54- 

L.  r.niblv. 
R.+0.5  45°- 

4/« 

•63 

F.  L. 

F.,  24. 

L.+4  C  +3  1  8o°- 
R.+2  C  +3  180.° 

4/24 
4/.» 

164 

A.  M. 

F.,  25. 

L.+o  5  90°. 
R.+O.S  90°. 

4/5 
4/5 

,65 

A.  W.  H. 

M.,  40. 

LH-o.5  i35°- 
R.+0.25  45°- 

V* 
4/4 

1  66 

J.  C.  P. 

M.,  30. 

L.+3- 
R.+2.25  C  +o-5  9°°- 

4/4 
4/5 

167 

J.S. 

M.,  16. 

L.  atnblyopic. 

R.+0.75  90°. 

4/5 

1  68 

S.  R. 

F.,  26. 

L.+0.5  90°. 
R.+  i.  90°. 

Vi 
*/4 

169 

S.  C. 

F.,  14. 

L  —3-5  C  —0-75  90°. 
R-—  3-5  C—  0.75  90°. 

4/5 

4/5 

170 

J.  McE. 

M.,  21. 

L.—  4  '0°. 
R—3C-I-  '70°. 

4/u 

4/b 

216 


STATISTICAL  RECORD. 


Num- 
ber. 

Name. 

Sex'  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

171 

D.  McE. 

M.,  21, 

L.+I.25  C  +3-5  5°°. 
R.+2  C  +4  105°. 

'/« 
Va 

172 

L.  M. 

M.,  50. 

L.—  6  C  —2-5  90° 
R.—  7C—  3  1  80°. 

V« 

Vu 

173 

T.  C.S. 

M.,  46. 

L.  —  0.75  1  60°. 
R.  Em. 

4/4 
V4 

174 

E.T 

M.>48. 

L.+075  90°. 
R.  Em. 

4/9 
*/• 

'75 

L.P. 

F.,  30. 

L.-f  as  1  10°  C  —0-75  20°. 
R.—  1.25  160°. 

*/5 
4/6 

176 

F.  G.  D. 

F.,  38. 

L.+0.75  70°. 
R.+0.75  1  10°. 

I 

177 

M.  M. 

F.,  16. 

L.+I-75  90°. 
R.+  I.  1  80°. 

* 

178 

A.  A.  F. 

F.,  15. 

L.+3- 
R.+o  75  90°. 

4/. 

V. 

179 

A.B.  S. 

M.,  45. 

L.—  i  C  —2-5  180°. 
R.—  0.75  180*. 

Vu 

4/» 

i  So 

S.  A. 

F.,42. 

L-+5-5  '35°. 
R-+I-75  45° 

4/» 

4/» 

181 

E.N.  W. 

M.,29. 

L.—  9C—  1-25  1  80°. 
R.  —  9  C  —1.25  180°. 

V. 

4/« 

182 

A.W. 

F.,9- 

L.+5.5  180°. 
R-+5  C  +3-5  90°. 

4/M 

Via 

183 

J,  li.  M. 

M.,25. 

L.—  0.75  1  80°. 
R.—  0.75  1  80°. 

4/4 

v« 

184 

M.  C. 

F.,  70. 

L.—  i  1  80°. 
R.  E.  (Com.  Cat.) 

4/« 

V* 

185 

A.  P. 

F.,  31. 

L.—  i  C  +i  160°. 
K-—  3-5  C—  2.5  1  80°. 

4/. 

V. 

186 

M.  G. 

F.,23. 

L.  —  2.25  C  —  i  90°. 
R-—  3-5  C  —i  90°. 

4/5 
4/6 

187 

M.  W. 

F.,39- 

L.—  i  1  80°. 
R.—  0.75  1  80°. 

4/» 

4/5 

1  88 

E.S. 

M.,  26. 

L.—  0.5  1  80°. 
R.—  0.5  180°. 

4/4 
V« 

189 

C.C.B. 

M.,  38. 

L-+7C-fi90°. 
R.-t-bC-fi  90°. 

4/~ 
V* 

APPENDIX. 


217 


Num- 
ber. 

Name. 

Hex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
Correction. 

190 

L.  J.  D. 

F.,  39- 

L.+  I.5  90°. 
R-+I-5  C  +5  90°. 

V5 
4/5 

191 

V.  E.  P. 

F.,  54- 

L.  Amblyopia. 
R-+I  C+075  1  80°. 

4/5 

192 

R.  G. 

M.,  21. 

L.  Atrophied. 
R.-fo.5  1  80°. 

V. 

193 

L,.  L 

F.,    12. 

L.—  0.73  1  80°. 
R.—  0.5  1  80°. 

V* 
«/< 

194 

S.  S.  W. 

M.,  26. 

L.  —  2.25  ;3  —  0.5  90°. 
R.  —  2.25  ^  —  0.5  90°. 

V4 
V* 

195 

J.  R.  M. 

M.,  33- 

L.—  0.5  10°, 
R.—  0.5  100°. 

% 

196 

C.  T. 

F.,  40. 

L.+I  115°. 
R.+0.75. 

•1: 

197 

A.  I.  D. 

M.,  57- 

L.+I  C  +°-5  9°°- 
R-+I  C  +0.5  90°. 

*/5 
4/5 

198 

D.  P.  G. 

M.,  15. 

L.+I  C  +0.75  9°°- 
R-+I  C  +°-75  90°- 

4/5 
4/5 

199 

A.  J.  G. 

F.,  50. 

L.  —  1.5  O  —  °-75  I2o°. 
R.  Amblyopia. 

4/5 

200 

M.  J.  S. 

M.,  63. 

L.—  5  C  —i  9°°. 
R.—  5  C  —i  9°°. 

4/12 
Vl* 

2OI 

J.H. 

M.,  43- 

L.—  0.75  45°. 
R.-9. 

4/9 
«/M 

202 

J.  S.  B. 

M.,  36. 

L.  —  0.75  C  —  1-5  "S0' 
R.—  0.5  50°. 

4/!8 
4/9 

203 

H.  C. 

F.,  40. 

L.  —  0.5  90°. 
R.—  0.5  90°. 

4/5 
4/5 

204 

M.  E.  M. 

F.,  50. 

L.-I  135°. 
R.—  i. 

4/12 
Vl2 

205 

R.  D.  K. 

F.,  40. 

L-+I-25  C+r-5'IIO°- 
R.  Em. 

4/9 
V* 

206 

H.  B.  C. 

M.,  29. 

L.  —4  C  —2-5  165°. 
R.—  6  C  —2  1  80°. 

4/6 
*/6 

207 

II.  C.  H. 

M.,  53- 

L.+0.7S  10°. 
R.+o.75ii5°. 

V* 
V* 

208 

H.  L. 

M.,  28. 

L.  2  C  2   15°. 

R.—  7s  C—  o-S  1  80°. 

4/6 
4/9 

218 


STATISTICAL    RECORD. 


A'um- 
ber. 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

209 

C.  F.  B. 

M.,  32. 

L.  Em. 
R.+0.5  170°. 

4/I 

210 

J.  H.  M. 

M.,48. 

L—  i  115°. 
R.  Em.  (Corn.  Cat) 

;/;; 

211 

S.  C.  McD. 

M,Si. 

I-+2C+0-75  180°. 
K-+0-75  C  +0.75  180°. 

v» 
4/» 

212 

M.  W.  R. 

K.,2,. 

1.—  1  C—  2  l8o°. 

R-—  '-25  C  —  0-75  180°. 

4/4 
V* 

213 

V.J. 

F.,  22. 

I..—  o.7s  1  80°. 
R.—  1.25  1  80°. 

y. 

2I4 

L.B.  S. 

M.,I3. 

I..—  i  180°. 
R.—  i  1  80°. 

v« 

4/4 

215 

J.  P.  J. 

M.,24- 

L—  0.5  180°. 
R.—  2.5. 

4/l 

216 

J.  P.  H. 

M.,43- 

L.+O.S  90°. 
R.—  0.5  1  80°. 

y* 

217 

A.  D.  R. 

M.,45. 

[-+0.5  45°. 
R.+o.5  135°. 

% 

218 

G.  M.  D. 

M.,52. 

L.-I.5'. 
R.—  i  C  —0-75  1  80°. 

vl 

219 

R.  N.  B. 

M.,  40. 

L.  emmetropia. 
R.—  0.75  1  80°. 

4/4 
4/4 

220 

M.   R. 

F.,  24. 

I..—  1.25  1  70°  C  +3-75  80°. 
U.—  0.75  10°  ^  +3.25  100°. 

Vn 

221 

CD. 

F.,  41. 

L.  —  3.5  ^  —  °-5  1  80°. 
R.—  4  C  —o-S  1  80°. 

•A 

222 

W.  F. 

M.,48. 

!>.  Em. 
R.—  0.5  90°. 

y* 

223 

C  C.  G. 

M.,s.. 

L.+0.75  90°. 
R.+O  75  90°. 

*/4 

V* 

224 

W.  H.  B. 

M.,  13. 

L.—  0.75  90°. 
R.  —  amhlyopic. 

*/* 

225 

E.E.  W. 

F.,  30. 

L,—  2.5  4So°. 

y« 

226 

H.  T. 

M.,4, 

I~—  .1-5  C  —0-75° 
R.—  8\ 

?i 

227 

M.  E.  M. 

F.,  15- 

L.—  i  ^  +0.5  90°. 
R.-H  C+28o°. 

y* 

APPENDIX. 


219 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision   after 
correction. 

228 

C.  M.  R. 

M.,  26. 

L.  —  amaurotic. 
R.—  8  C  —i  1  80°. 

4/6 

229 

C.  T. 

F.,  30. 

L.—  0.75  180°. 
R.—  0.75  180°. 

V5 
4/5 

230 

F.  S. 

F,   12. 

L.—  0.5  1  80°. 
R.—  0.5  1  80°. 

4/4 
V* 

231 

B.  C  . 

F.,    12. 

L.—  2.5  1  80°  C  +4  90°- 
R.+4  90°- 

Vn 

Vl2 

232 

A.  H.  W. 

F.,  1  8. 

L.—  45  C  -i-5  85°- 
R.—  45  C  —2  90°. 

4/6 
4/6 

233 

N.  G. 

F.,  1  6. 

L.—  2.5  C  —0-5  80°. 
R.—  0.5  90°. 

4/9 
4/6 

234 

J.  H.  McB. 

M.,  40. 

L.—  i  90°. 
R.-i.S  95°. 

4/9 
4/6 

235 

A.  R. 

F.,   20. 

L.—  0.5  90°. 
R.—  0.5  90°. 

V* 

4A 

236 

B.  P. 

F.,  25. 

L.—  i  180°. 
R.—  i  1  80°. 

4A 

4/4 

237 

D.  B. 

F.,  1  6. 

L.  —  0.5  O  —  0.75  1  80°. 
R.—  0.75  C  —0.75  180°. 

4/5 
4/5 

238 

D.  T.  W. 

M.,  33. 

L.—  2.75  C  —  1-5  I00°. 
R.—  3.5  C  —i  I00°. 

4/5 
4/5 

239 

H.  H. 

M.,  1  8. 

L.-fo.75  1  80°. 
R.+0.75  180°. 

4/6 
4/6 

240 

E.  P.  H. 

M.,  49. 

L.—  i  C  —0-5  180°. 
R.  amblyopic. 

V5 

241 

J.  M.  E. 

F.,  34- 

L.+0.5  90°. 
R.+0.75  90°. 

4/9 
4/9 

242 

A.  M.  M. 

M.,  38. 

L.—  0.75  180° 
R.—  0.75  1  80°. 

V* 
4/4 

243 

R.  K. 

M.,  50. 

L.+I.  1  80°. 
R.  amblyopic. 

4/6 

244 

W.  W. 

F.,  38. 

L.—  0.5  135°. 
R.-O.S  45°- 

4/4 
4/4 

245 

G.J.    ' 

M.,  38. 

L.  —  0.75  90°. 
R.—  1.25  90°. 

*/5 
4/5 

246 

M.  M. 

F.,  48. 

L.-0.75  135°  C  +0-75  45°- 
R.—  0.75  45°  C  +0-75  i35°- 

4/6 
4/6 

220 


STATISTICAL    RECORD. 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
af  axis  of  cylinder. 

*ision  after 
correction. 

247 

C.  W.  S. 

F.,  30. 

L.—  0.5  1  80°. 
R.—  as  180°. 

«/4 

v« 

248 

F.  L.G. 

F.,  16. 

L.—  0.5  1  80°. 
R.—  0.5  180°. 

Vi 

«/4 

249 

P.  X.D. 

M.,4i. 

L.+.M  90°. 
R.+2.5  90°. 

v« 
•/•I 

250 

L.  H. 

F.,  1  8. 

L.—  0.5  1  80°. 
R.—  0.5  1  80°. 

V* 

4/4 

251 

I.  W.  B. 

M.,40. 

L.  —  0.5  1  80°. 
R.—  0.5  1  80°. 

*/l 

*/5 

752 

J.  S.  B. 

F.,  48- 

L.+075350- 
R.+0.75-. 

4/6 
4/6 

253 

D.B. 

F.,  18. 

L.—  3C—  °5  "80°. 
R.—  3  C  —  o  5  1  80°. 

'/• 

'/• 

254 

E.  M. 

F.,  25. 

L.+0-5  175°. 
R.+0.5  180°. 

•/« 

v« 

255 

J.  J.  A. 

M.,40 

L  —  0.5  40°. 
R.—  Em. 

*/. 

256 

E.S. 

F.,  21. 

L.  Em. 
R.-0.7S  90°. 

V. 

257 

r.  s. 

?.,  26. 

L.—  0.75  50° 
R.  —  0.75  140°. 

4/» 
•/• 

258 

K.  J.  F. 

F.,  40. 

L.+0.75  135°. 
R.+0.75  45°. 

4/5 
4/5 

259 

K.  B.  F. 

F.,  40- 

L.—  a  5  1  80°. 
R.—  0.5  180°. 

4/« 
4/4 

260 

C  E.  P. 

F.,  30. 

L.—  a  5  1  80°. 
R.—  0.5  15°. 

4/» 
4/» 

261 

K.  B. 

M.,3i. 

L.—  i  70°. 
R.—  i  110°. 

*/• 

V. 

262 

CS. 

F.,  30- 

L.—  05  180°. 
R.—  0.5  180°. 

% 

263 

M.  W. 

F.,  65. 

L—  ioc. 

R.—  6C—  i  90°. 

ft 

264 

E.L. 

F.,  i& 

L.+OJ5  90°. 
R.+0.5-. 

4/4 
4/» 

265 

H.  E. 

F.,  18. 

L.+0.75  90°. 
R.+0.75  9°°- 

4/5 
4/5 

APPENDIX. 


221 


Num- 
ber. 

Name. 

ex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

rision  after 
orrection. 

266 

-H.. 

.,  29. 

u.—  0-5    1  80°. 

R..—  0.5  180°. 

4/5 
4/5 

267 

.H. 

VI.,  45- 

L.—  0.25  135°. 
R..—  0.5  45*.                        f 

^ 

268 

R.  G. 

.,  18. 

L.—  0.5'. 
R.—  0.5  1  80°. 

^ 

269 

.H.  H. 

•f  34- 

L-+I-75  C  +i  90°. 
R.+I-75  C  +i  90°. 

4/5 

270 

L.  B. 

F.,  21. 

L.+O.S  95°. 
R.+O.S  85°. 

4/4 
4/4 

271 

W.  R.  W: 

F.,  25. 

L.—  12s. 
R.—  12  C  —I- 

V» 

272 

J.  H.  W. 

M.,  28. 

L,—  6  C  —I  90°. 
R.—  8  C  —I  90°. 

4/6 
4/6 

273 

G.  W. 

M.,SI. 

L.+3  180°. 

R.+2  1  80°. 

Ve 

274 

A.  L. 

F.,  16. 

L.—  i.SC—  o-545°-o 

4/4 

275 

F.  S.  P. 

M.,  26. 

£i  ST^1;  A 

4/5 
4/5 

276 

J.  S.  B. 

M.,50. 

L.+P. 
R.+I  C  +0.5  1  80°. 

4/I 

277 

J.L. 

F.,  20. 

L.—  0.75  90°. 
R.-0.75  90°. 

v* 

278 

F.  W.  I. 

M.,27. 

L.+0.5  90°. 
R.+O.S  90°. 

4/4 
4/4 

279 

C.  A.  P. 

M.,45- 

L-+I  Q,+0-s- 

;//; 

280 

C.  A.  N. 

F.,  26. 

L.—  0.75  180°. 
R.—  0.75  180°. 

4/l 

281 

L.  A. 

F.,  21. 

L.+0.75  i35°- 
R.+0.75  45  • 

4/4 
*/4 

282 

D.  E.  S. 

F.,  30. 

L.-i.s  90°. 
R.—  2.5  90°. 

4/4 
4/5 

283 

L.  B. 

F.,   12. 

L.—  4. 
R.—  3C—  1-5  l8o°- 

4/9 
4/9 

284 

M.  V. 

F.,  13. 

L.+i  100°. 
R,+i  80°. 

% 

222 


STATISTICAL    RECORD. 


Num 
ber. 

285 

Name. 

Sex  and  Age 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

M.  L.S. 

F.,  40. 

L.+l8oC. 
R-+0.75  95C- 

y* 

286 

S.C 

F.,  36- 

L.+0.7S  9°°- 
R.+O.75  90°. 

;/« 

287 

W.  F.  R. 

M.,22. 

L.—  0.5  1  80°. 
R.—  0.5-. 

% 

288 

E.M. 

F.,  50 

L.+0.75  l8o°- 
R-+I  C  +0.75  180=. 

4/e 
4/« 

289 

E.P. 

F.,  3°. 

L.+2-5  90°. 
R.-J-2.5  90°. 

;/. 

290 

J.  P.  M. 

M.,53- 

L.  —  10  C  —  *  175°' 
R.—  10  C—  i  10°. 

y. 

291 

E  S.  P. 

M.,40. 

I  0.75  180°. 
R.—  0.75  1  80°. 

4/5 

4/b 

292 

C.W.  F. 

F.,  3°- 

L  —  0.75  180°. 
R.—  o  75  180°. 

4/l 

293 

J.  H.  W. 

F.,  40- 

L.-J-25  C  +o  5  100°. 
R.+i  C  +i  90°. 

;/; 

294 

A.  S. 

F.,  21. 

L  +0.75  180°. 
R.  Em. 

% 

295 

J.  O.  S. 

M.,  48. 

L.  Em. 
R.+2  25  ^  +0.5  100°. 

•     4/s 

296 

1*»  -M  .   1  '. 

F,  40. 

L-+I-75  C  +0.5  9°°- 
R-+'  75  C  +o-5  90°. 

4/5 
4/5 

297 

C.A.  H. 

M,30. 

L—  0.75  C  —0-75  60°. 
R.  —  0.5  ^  —  °-5  120°. 

4/5 
4/5 

298 

K.  S. 

F.,  17. 

L  —  0.5  40°. 
R.—  0.5  180°. 

4/5 
4/5 

299 

S.  A. 

F.,  42. 

-  +0.75  100°. 
R  +0.75  180  . 

J/4 

300 

W.  H.  K. 

M.,  23. 

L—  3-5  C  i  -5  '55°. 
R.—  4-5s. 

4/J 

301 

E.  W.  N. 

F.,  40. 

i.^5  C  —  i  20°. 

4/» 

302 

J.  B.  B. 

M.,50. 

..+2.25p  +0.75  30°. 

V; 

3°3 

D.  E.  S. 

M.,36. 

L—  1.5  i  So  . 
R.—  i  170  . 

4/4 

4/4 

APPENDIX. 


223 


Num- 
ber. 

0 

Name. 

Sex  an    Age. 

Correcting  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

3<>4 

H.  W.  G. 

F.,35- 

L.—  0.75  180°. 
R.—  0.75  1  80°. 

4/4 
V* 

3°5 

W.  A.  K. 

M.,4i. 

L.—  i  C  —2  180°. 
R.—  1.5  1  80°. 

4/9 
V9 

306 

T.  B.  M. 

M.,23- 

L.  —  0.5  90°. 
R.  —  0.75  100°. 

4/5 
4/6 

307 

R.  R.  W. 

M.,33- 

L.  Amblyopic. 
R.-0.5  180°. 

V* 

308 

E.  C. 

F.,  17. 

L.+0.75  90°. 
R.—  1.25  180°. 

4A 

4/5 

309 

J.  B.  K. 

M.,  14. 

L.—  <;  1  80°. 
R.—  5  1  80°. 

4/l* 
4/12 

310 

T,  C. 

M.,  25. 

L.—  0.75  1  80°. 
R.—  0.75  1  80°. 

V' 
V* 

3" 

J.  F.  K. 

M.,  43. 

L.—  0.75:180°. 
R.  Em. 

4/4 

312 

A.  M. 

F.,  21. 

L.  Em. 
R.—  0.75  180°. 

V* 

v« 

313 

M.  L. 

F.,  21. 

L.—  2  C  —  2.5  130°. 
R-—  4  C  —i-5  130°. 

Vl8 
4/24 

3H 

S.  M.  B. 

M.,40. 

L.  +2.5  70°. 
R.Em. 

Vl8 
4/4 

315 

K.  A. 

F.,  12. 

L—  4  10°. 
R.—  4  1  80°. 

'V18 
Vl8 

316 

L.  J.  B. 

M.,45. 

L.+3-5   C  +I.2S  160°- 
R.+4  C  -f  i  1  80*. 

*/9 
Vl2 

317 

H.  C.  L. 

F.,  33- 

L+2C+'  165°. 
R.+2  C  +1  15  • 

4/5 
4/5 

3i8 

W.  B.  H. 

M.,  23. 

L.—  0.5  180°. 
R.  —  0.5  i8ov. 

4/4 
4/4 

3'9 

C.  N. 

F.,  22. 

L.—  2    1  80°. 
R.—  2    1  80°. 

% 

320 

H.F. 

M.,33- 

L.—  0.5  20°. 
R--0.5  '55°- 

% 

321 

S.  P.  T. 

F.,  40. 

L.  —  4  140°. 
R.—  4  165°. 

4/6 
4/24 

322 

M.  W. 

F.,  1  8. 

L.+6  105°. 
R.+2  1  80°. 

4/36 
4/9 

224 


STATISTICAL  RECORD. 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correcting  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

323 

S.  R.  B. 

F.,40. 

L.-0.75. 
R.—  0.5  100°. 

;/. 

324 

F.  0. 

F.,  18. 

L.—  0-5  35°- 
R-+0-5  30°. 

4/« 
4/« 

325 

A.  P. 

F.,  55- 

L.+3- 
R.+I-75  C  +0-75  90°. 

;/; 

326 

M.  L.  F. 

F.,  21. 

L.+O.S  180°. 
K.+0.7S  '80°. 

j/t 

327 

J.C. 

F.,  17. 

L.+I.25  120°. 

R.  +0.75  90°. 

V;/; 

328 

D.  M.  O. 

M.,  38. 

L.—  as  90°. 
R.—  a25  90°. 

v« 

V* 

329 

N.  H. 

F.,  13- 

L.  Em. 
R.—  2.25  1  80°. 

4/u 

33° 

A.B. 

F.,30. 

L.-0.75  30°. 
R.—  2.5. 

V. 
V. 

33i 

M.  B. 

F.,  14. 

L.—  3-5  C  —0.5  90°. 
R.-3-5- 

% 

332 

M.  D. 

F.,  13- 

L.  +10  0+0.75180°. 
R.+IO  C  +0-75  1  80°. 

v! 

333 

J.J.J- 

M.,47- 

L.4-I- 

R-+2-5  C  +1   120°. 

vl 

334 

B.  A.  P. 

F.,  45- 

L.—  12. 

R.—  8  C  —i  145°. 

;/» 

335 

J.  M.  K. 

M.,  26. 

L.4-0-75  105°. 

R.—  2. 

% 

336 

R.  J.  M. 

M.,32. 

L.—  6  C  —i  180°. 

R.—  2. 

\u 

337 

W:F.  M. 

M.,47. 

L.4-0.5  90°. 
R.4-0.5  90°. 

vl 

338 

D.  B.  S. 

F.,  45- 

I  0.5  180°. 
R.—  0.75  135°. 

4/4 
4/4 

139 

A.T. 

F.,  19- 

L.  Em. 
R.4-as  115°. 

4/4* 

M. 

L.S.B. 

M.,  23. 

I  —  1.75  170°. 
R.—  1.25. 

4/4 
V* 

Hi 

M.  F. 

F.,  50. 

L.+3  '80° 
R.+2.25  C  +0.75  180°. 

4/«o 
Vs 

APPENDIX. 


225 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

^ision   after 
correction. 

342 

H.  B.  B. 

F.,46. 

-•+!-5  C+°-5  9°°- 
R..  Aniblyopic. 

4A 

343 

L.  N. 

F.,    20. 

L.—  10  C—  0-5  180°. 
R.—  9C—  0-5  1  80°. 

4/6 
4/9 

344 

E.  R.  B. 

F.,  40. 

L-+I-5  C  +0.5  90°. 
R-+I.  C  +0.5  90°. 

V4 

345 

A.  W. 

F.,  19. 

L.—  0.75  1  80°. 
<..—  Em. 

;/4 

346 

E.  B. 

F.,  28. 

L.-I.5  135°. 
R-—  1-5  C—  1-5  45°- 

4/5 
4/5 

347 

D.  S. 

M.,  33- 

L.+2.25  O  +  !-5  I2o°. 
R.+2.5- 

4/92 

348 

S.  C. 

F..  38. 

L.—  4.  C—  o-75  180°. 
R-—  3-5  C—  0.5  180°. 

4/5 
*/• 

349 

E.  F. 

F.,  39- 

L-+2-5O+I  170°. 
R-+2-5O+I  180°. 

Vl8 

35° 

G.  C.  K. 

F.,  50. 

L.+445°- 
R+o.sO  +  i  90°. 

;/i8 

35- 

D.  C. 

F.,  41. 

L.—  1.5  1  80°. 

R.—  2  1  80°. 

;/5 

352 

C.  H.  M. 

M.,  40. 

L.—  0.5  20°. 
R.—  0.5  140°. 

\ 

353 

M.  A. 

F.,  18. 

L.—  0.50  —°-75  1  80°. 
R.—  1.5  C—  0.75  180°. 

i 

354 

M.  W.  R. 

F.,  40. 

L.+2  140°. 
R.+i  10°  C—  1-5  100°. 

4/5 
4/6 

355 

E.  M. 

F.,  48. 

L.  —  2  io°O+4-75  100°. 
R—  2  I70C+5  80°. 

4/98 

356 

N.  M. 

F.,  50. 

L.  —  0.5  90°. 
R.  —  4  O  —  0.5  90°. 

4/5 
4/9 

357 

A.  T.  B. 

M..SI. 

L.—  4O—  i  7o°. 
R.—  4O—  i  130°. 

% 

358 

M.  A. 

F-,  45- 

L  —  0.5  90°. 
R.-4- 

4/u 

.159 

M.  W. 

F.,  50. 

L.  —  i  O  —  0.75  60°. 
R.—  r  C  —0.75  120°. 

%- 

360 

B.C. 

F.,  36. 

L.+2  O  +0.5  QO°- 
R.  +0.75  90°.  ' 

;/: 

226 


STATISTICAL    RECORD. 


Num 
her. 

Name, 

Sex  and  Age, 

Correction  Glasses  and  direction 
of  axis  of  cylinder. 

Vision  aftet 
correction. 

.#1 

E.T.  P. 

M.,48. 

L.  Amblyopic. 
R.+0.5  90*. 

*/• 

v« 

362 

E.J. 

F.,  50. 

I-+2  C  +o  5  5 
K.+2C+0-5  '75°- 

V* 

v« 

363 

L.P. 

F.,  38- 

L.+2.5  C  +o  5  i8oP. 
R-+2-5C+0.5  i8<P. 

*/4 
*/4 

364 

A,  D.  J. 

M.,43. 

L.4-I. 

R.-fo-S  C  +0.5  1350. 

V* 

v« 

365 

A.W. 

M.,  15. 

L.  —  075  C  —  0.5  90-. 
R.  —  i  C  —  0.5  90-. 

4/4 
V5 

366 

A.  McG. 

F.,  17- 

L.—  0.5  180°. 
R.—  0.5  180°. 

V« 
4/4 

367 

J.  S.  H. 

M.,32. 

L.+0-5  gcP. 
R.+0.5  900. 

4/4 

v« 

368 

M.  E.  G. 

F-,  33- 

L—  4C  1-5—  i8cP. 
R.-4. 

*/• 

V» 

369 

J.  M.  C. 

F.,  1  8. 

L.  —  0.5  1  00°. 
R.—  2.25. 

4/4 
V* 

370 

N.  H. 

F.,  26. 

L.—  i. 
R—  2.5  C  —2  90°. 

*/4 
4/5 

371 

P.  M. 

F.,  1  8. 

L.+0-5  90°. 
R.-f  0.5  90°. 

*/4 
*/4 

372 

M.  L.  N. 

F.,  31. 

L-I4S0- 
R+o.5  90°. 

4/4 
4/4 

373 

H.  T.  H. 

F.,  40. 

l«  Km. 
R.+I  90°. 

4/4 
V« 

374 

J.L.J. 

M.,46. 

L.+°.75  135°- 
R.+a75. 

V* 
4/5 

375 

VV.  D. 

F.,  24. 

L.  Em. 
R.—  CX5  90°. 

4/4 
4/4 

376 

S.  B.  M. 

F.,  27. 

1..—  0.5  1  80°. 
R  —  0.5  1  80°. 

4/4 

377 

C.  A.  K. 

M.,  27. 

R.+4  i?o°C—  390°. 
R  —  6  90°  (keratoconus). 

Vl2 
4/» 

378 

N.  R. 

F.,  14. 

L.+0  75  1  80°. 
R.+0.75  180°. 

4/4 
V* 

379 

J.K. 

M.,70.                   0.5  180°. 
K.  Em. 

4/6 

APPENDIX. 


227 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
af  axis  of  cylinder. 

Vision  after 
correction. 

380 

M.  V. 

F.,  1  6. 

L.+4-5  95°- 
R—  i  1  75°  0+2.585°. 

4/6 
*/6 

38i 

A.D. 

F.,  14- 

L.  —  4. 
R.—  0.5  170°. 

4/9 
V4 

382 

A.S. 

M.,  42. 

L.+0.75  90°. 
R.+o-s  90°. 

4/4 
*/4 

383 

S.  W.  C. 

F-33- 

L.+6  C  +3  I35°- 
R.+2  5  C  +4-5  9°°- 

*/• 

Vu 

384 

H.  W.  H. 

M.,26.            IL.—  0.5180°. 
IR.—  0.5  1  80°. 

4/4 
4/4 

385 

J.  W. 

F.,  5°. 

L  +1.25  1  00°. 
R  +1.25  170°. 

4/4 
V* 

386 

A.  H. 

M.,  44. 

L.—  0.5  45°- 
R-—  0-75  i35°- 

4/4 
4/4 

387 

E.  L. 

F.,  1  8. 

L.—  2. 

R-—  0.5  C—  5  1  80°. 

4/4 
4/4 

388 

L.J. 

M.,2g. 

L.—  o  5  80°. 
R.—  0.5  100°. 

4/4 
4/4 

389 

W.  M.  G. 

F.,  50. 

L--f  -o  75  C  +4-5  90°. 
R-+0.75  C  —3-5  90°. 

4/5 
4/5 

390 

L.  H.  C. 

F.,  36. 

L.+3  90°. 
R.—  3  150-. 

Vo 
4/. 

391 

S.  F. 

F.,  50. 

L.+i. 

R.+Q.5  C  +o.75°- 

4/5 
4/5 

392 

L.  G. 

F,  18. 

L.+i. 
R.+i  C  +°-5  9°°- 

% 

393 

E.  L. 

M.,  19. 

L.  Em. 
R-  —  1-5  C—  0.5  90°. 

% 

394 

J.  B.  M. 

F.,  38. 

L.  Em. 
R-—  1-5  C—  1-25  1  80°. 

Vl8 

395 

S.  C. 

F.,i7. 

L.-f  0.75  90°. 
R.  Em. 

4/4 
4/4 

396 

H.  W.  S. 

F.,  28. 

L.+  i  -25  90°. 
R-+4-5  9°c- 

Vo 
4/18 

397 

A.  M. 

F.,2I. 

L.+4  90°. 
R.+IC+I-5  90°. 

Veo 

4/5 

398 

A.  O'C. 

F.,  32. 

L+4C+29°°. 
R.+3  5  C+2  90°. 

4/4 
4/4 

228 


STATISTICAL  RECORD. 


Num 
ber. 

Name. 

1 

Sex  and  Age 

Correcting  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

399 

K.H. 

F,  50. 

L.-I.5  15°. 
R.—  i  180°. 

v« 

V* 

400 

H.  H.  N. 

M.,48. 

L.-f  1.590°. 
R.+I.900. 

% 

401 

I.  R. 

F.,  1  6. 

L.—  i  180°. 
R,—  i  180°. 

4/l 

402 

H.  M.  I.         F.,  33. 

L.—  i  C—  0.5  1  80°. 
R.—  0.5  180°. 

;/i 

403 

O.I. 

M.,47. 

L.+0.5  90°. 
R.+as  90°. 

y* 

404 

li.  K. 

F.,  36- 

L.+3.5  105°. 
L.+4-5  70s. 

y.8 

405 

C.  B. 

F.34- 

L.+5-5  90°. 
R-+3  90°. 

;/;: 

406 

T.  K.  S. 

M.,47.             I  ..+0.5  90°. 
R.+6ioo°. 

;/4 

407 

A.N. 

F.,  19.             L.—  4.5  C  —1.25  180°. 
;R.—  4-5  C—  o-S  I90°. 

4/4 
4/4 

408 

G.  M.  W. 

M,26. 

L.  —  0.75  90°. 
R.—  0.5  90°. 

;//; 

409 

F.  B.  N. 

M.,  28. 

L.  —  0.75  90  . 
R.  —  0.75  90°. 

4/5 
4/5 

410 

S.  F. 

F.,  29. 

L.+I  C  +4-5  90°. 

R-+5  90°. 

4/9 
*/• 

411 

G.M. 

M.,36. 

L.—  3O—  3-5  45C- 
R.  —  4  ,  ,  —  2  90^. 

v" 

412 

L.H. 

F.,  27. 

L.—  0.75  180°. 
R.—  0.75  1  80°. 

4/s 
•/• 

413 

L.  B. 

F.,  10. 

L.+2.5  95°. 
R.+3950- 

;/5 

414 

I.I. 

F.,    21. 

[  0.5  1  80°. 
R.—  0.25  180°. 

y* 

415 

N.  P.  S. 

F.,  23. 

L.+'  C+o.5  90°. 
R-+I  O  +0.75  90°. 

4/4 
4/4 

416 

H.  A.  C. 

F.,  50. 

L.—  i  O  —0.5  45°. 
R.—  as  90°. 

;/: 

417 

C.S.J. 

M.,35- 

-+2O+I    90°. 

R.  +2C+  1  45°. 

V; 

APPENDIX. 


229 


Num- 
ber. 

418 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

C.  M. 

F.,  21. 

L.—  i  1  80°. 
R.—  I   1  80° 

4/4 
.    V4 

419 

K.  H. 

F.,  20. 

L—  4C—  1-25  30°. 
R.—  4C—  0-75  150°. 

Vi 
V* 

420 

M.F. 

F.,  56. 

L.+2  C  +i  80°. 
R-+2  C  +i  90°. 

4/5 
V5 

421 

K.  B. 

F.,  50. 

L.+2  C  +2-5  100°. 
R-+I-5  C  +i-5  100°. 

V* 
*/« 

422 

M.  T. 

F.,  27. 

L.+0.5  90°. 
R.+0.5  90°. 

4/4 
V* 

423 

C.  M. 

F.,  40. 

L.-J-0.5  115°. 
R.  E. 

4/4 
*A 

424 

L.  T.  L. 

F.,  30. 

L.  —  3  c;  —  0.75  90°. 
R.—  3  C  —0-75  90°. 

*/5 
V5 

425 

A.  G.  R. 

M.,  23. 

L.—  2.5  C  —0.75  10°. 
R-—  35C—  0-75  ^o0- 

4/5 
Vo 

426 

E.  G. 

F.,  38. 

L.  E. 
R.  —  0.75  1  80°. 

% 

427 

E.  F. 

F.,  50. 

L.  —  0.5  1  00°. 
R.—  0.5  80. 

% 

428 

W.  H.  S. 

M.,  17. 

L.—  0.5  1  80°. 
R.  E. 

4/6 
V* 

429 

J.  L.  M. 

F.,  48. 

L.  E. 
R.—  1.5  175°. 

4/4 
4/5 

43°* 

M.  L.  T. 

F.,  35- 

L.—  1.5  1  80°. 
R.—  2.25  1  80°. 

V* 
4/5 

43i 

L.  T. 

F.,  40. 

L.-I.J  135°. 
R.-0.75  45°- 

4/5 

4A 

432 

M.  E.  O. 

F..  48. 

R.—  0.75  90°. 
R.  E. 

4/4 

4A 

433 

C.  C. 

F.,    21. 

L.+I-5  110°. 
R.—  0.5  180°. 

4/5 
4/4 

434 

A.  D.  H. 

M.,44. 

L.  —  0.5  100°. 
R.—  0.5  80°. 

4/6 
V« 

435 

F.  R.  G. 

M.,  25. 

L.—  0.75  C  —0-75  75°- 
R.—  C  —0.75  105°. 

4/5 

4/5 

436 

L.  A. 

F.,  42. 

L.+O-S  80°. 
R.+o-S  100°. 

4/4 
4/4 

230 


STATISTICAL    RECORD. 


Num- 
ber. 

Name. 

Sex'  and  Age. 

Correction  glasses  ami  direction 
of  axis  of  cylinder. 

Vision  after 
correction. 

437 

N.A. 

F.,  .31. 

L.-5- 
K.—  4.5  C  —o-5  iko°' 

v« 
'/• 

438 

T.  M. 

F.,  53- 

L-+3C+I  50°. 
R.+  '-5C  +i-5  90°. 

Vu 

V* 

439 

C.  A.C. 

F.,  50. 

L-+I-5  C  +o-5  i3°°- 

R.+2.25. 

4/5 

«/• 

440 

A.J. 

F.,  36- 

L.+3-5  C  +0.75  90°. 
R-+3-5  C  +0.75  90°. 

V* 

«/4 

441 

A.  R. 

F.,42. 

L.+  I. 

R-+3  C  +2:90°. 

4/4 
4/« 

442 

G.  R.  G. 

F.,  33- 

L.  —  as  20°. 
R.-I  155°. 

V4 
V5 

443 

W.  D.  J. 

M.,  25. 

L.+0.5  90°. 
R.-fo.S  90°. 

*/4 
4/4 

444 

C.  E.  R.      . 

M.,  40. 

L.+0-5  90°. 
R.+os.  90°. 

4/4 
V* 

445 

M.  L. 

M.,  21. 

L.—  3C—0.5900. 
K.—  3  C  -0.5  90°. 

V* 

V* 

446 

N.  B. 

F.,  1  8. 

L.—  as  1  80°. 
R.—  i"i8o°. 

V* 
4/4 

447 

M.  B. 

F.,  19. 

L.—  0.75  1  60°. 
R.—  0.5  10°. 

4/4 
4/4 

448 

L.S. 

F.,  17- 

L.  —  2  C  —  0.5  35°. 
R.—  i  C  —0.5  180°. 

4/4 
4/4 

449 

V.  H. 

M.,  17. 

L.-3  Q  -0.5  55°. 
R—3- 

4/5 
4/5 

450 

J.  T.  K. 

M.,  21. 

L-—  7C—  0-75  '80° 
R.-7. 

4/4 
V* 

45» 

M.  C.  T. 

M.)48. 

L.—  6  C  —i  60°. 
R-—  4C—  0.5  75°. 

4/4 
4/4      . 

452 

B.  B. 

F.,  17. 

L.  —  1.5  3  —0.75  180°. 
R.—  1.5  C—  0-75  1  80°. 

4/4 
4/4 

453 

B.  S. 

M.,  19. 

L:  —  i  C  —  0.5  90°. 
R.—  i  C  —o-S  90°. 

4/4 
4/4 

454 

S.  C. 

M.,  21. 

L—  0.5  1  80°. 
R.—  0.5  1  80°. 

4/4 
4/4 

455 

J.H. 

M.,  17. 

L.+as  90°. 

R.+2. 

4/4 
4/» 

APPENDIX. 


231 


Num- 
ber. 

Name. 

Sex  and  Age. 

Correction  glasses  and  direction 
of  axis  of  cylinder. 

Vision   after 
correction. 

456 

J.  M. 

M.,  46. 

L.+  i  80°  ^  —  2  170°. 
R.-f  i  90°  C—  2  1  80°. 

4/5 

457 

M.  D. 

F.,  15. 

L.+0-5  90°. 
R.+0-5  90°. 

I 

458 

G.  S. 

F.,  28. 

L.+2.2S  C  +0.5900. 

R.—  2.25  3  +0.5  90°. 

V4 

459 

H.  C.  F. 

F.,  50. 

L.+0.5  1  80°. 
R.+o.s  1  80°. 

$ 

460 

A.  S. 

M.,  71,    * 

L.+  i  C+o-5  90°. 
R.  —  Amblyopic. 

4/5 

461 

J.B 

M.,  15. 

L.  E. 
R.-f  0.5  110°. 

4/5 

462 

M.  F. 

F.,  30. 

L+i  C+i  90°. 
R.+i.S. 

% 

463 

A.  A. 

F.,  20. 

L.  —  2.5  c  —  0.5  ioo°. 

R.  —  2.5  C  —  0.5  100°. 

% 

464 

P.  J.  M. 

M.,  40. 

L.+4  C  +i  1  80°. 
R.+0.5  1  80°. 

.;/;* 

465 

E.  C. 

F.,  41. 

L.  +  i  C  +2.5  90°. 
R.+i  C  +2.5  90°. 

4/5 

466 

M.S. 

F.,  25. 

L.—  0.7  s  10°. 
R.—  0.75  170°. 

;j; 

467 

Wm.  S. 

M.,  33- 

L.—  1.25  180°. 
R.—  0.5  1  80° 

:'/: 

468 

G.  P. 

F.,  1  8. 

L.  +  i  170°. 
K.—  i. 

4/12 

469 

C.  C.  j. 

F.,  26. 

L.-j-i90°C—  3  1  80°. 
R.+i.590°C—  4  1  80°. 

4/9 

•470 

G.  W.  K. 

M.,  57- 

L.+O.S  45°. 
R.+0.75  135°. 

:/;; 

47! 

J.  W.  H. 

F.,  40. 

L.+i  c  +i  90°. 
R.  E. 

vt 

472 

A.  S. 

F.,  36. 

L.+0.5  135°. 
R.  E. 

v* 

473 

H.  S 

F-,  13- 

L  —  05  180°. 
R  —  0.5  1  80°. 

V* 

NBA     AND     CORRIGENDA. 


Beginning  at  the  ninth  line  from  the  top,   page   34,    for  "one 
of  these   represents,    etc.,"  read:     "The   first  of  these 
tables  shows  the  focus  of  a  lens  of  100  inches   focus 
for  every  5°  of  rotation  on  its  vertical  axis,  in  the  ver- 
tical meridian.     The  second  table   shows   the  focus  in 
the  horizontal  meridian."    In  the  table,  for  "hoiizontal 
inclination,"  read    "vertical  meridian,"  and  for  "ver- 
tical inclination"  read  "horizontal  meridian." 
Page  36.— 9th  line  from  top,  for  "— 7^"  read  "+7^." 
Page  41. — The  "8"  at  the  bottom  and  to  the  left  of  the  diagram 

should  be  "—3." 
Page  74. — 18th  line  from  the  top,  for  "hydrochlorate"  read  "hy- 

drobromate." 

Page  96. — 8th  line  from  top,  insert   "horizontal"  before   "me- 
ridian.'' 

Page  131. — 2nd  line  from  top,  for  "larger"  read  "longer." 
Page  162 — 25th  line  from  top,   insert  "right"  before    "angles." 
Appendix. — 1st  and  4th  linos  for  "475"  read  "473." 
Appendix. — 4th  line  from  the  top,  for  "41  per  cent."  read  "15 

per  cent." 

The  test-types  and  fan  of  Snellen  used  for  diagnostic  pur- 
poses can  be  obtained  from  Meyrowitz  Bros.,  New  York;  Queen 
&  Co.,  Philadelphia,  or  other  prominent  opticians. 

The  refraction  ophthalmoscope  with  attachment  for  cylinders 
described  on  page  99  et  xeq.  may  be  had  of  James  W.  Queen 
&Co.,  Philadelphia,  who  can  also  attach  a  clip  for  holding  the 
cylinders  to  most  of  the  refraction-ophthalmoscopes  in  common 
use. 


4/VI 

1    <! 


INDEX. 


A 

Accommodation  in  aphakia,   possibly  due    to   astig- 
matism, 65 
partial,  in  childhood,    -  140 
to  what  due,    -  65 
influence    of  on  Astigmatism,  66 
producing  irregular  astigmatism,  182 
Airy's  changes  in  form  of  a  point  of  light  in  astigmatism,       74 
case  of  astigmatism,    -  156 
Ametropic  eyes  compared,    -  49 
eye.      -  49 
Angle  of  retraction,  laws  governing,  2 
Aphakia,  accommodation  in,  65 
Astigmatic  fundus,  artificial  demonstration  of,  98 
likely  to  be  mistaken  for  neuroretinitis,     97 
view  of,     -  97 
Astigmatics,  characteristic  mistakes  of,  $6 
Astigmatism  from  blows  on  the  eye,  150 
iritis,  -  150 
dislocation  of  the  lens,  150 
abnormal,  3^>4^ 
compound,        -  S1 
definition  of,    -  I 
derivation  of  the  term,  14 
determination  of  its  existence,  59 
diagnosis  of,     -  55 
forms  of.  5° 
of  the  horizontal  corneal  meridian,  -         39,40,41,42 
influenced  by  accommodation,  66 
mixed,  51 


234  INDEX. 

name  given  by  Whewell,  158 

normal,  38 

regular  in  the  human  eye,  -  43,  44 

simple,  50 

Asthenopia,  astigmatic,  143 

astigmatic,  illustrative  case  of,  142 

illustrative  case  of,  -  142 

in  astigmatism,  141 

muscular,  141 

on  what  it  depends,  -  141 

nervous,  143 

often  absent  in  high  degrees  of  ametropia,  -  141 

worse  when  the  meridians  are  oblique,  _  143 

Atropine,  indications  for  the  use  of,  71 

use  of  in  diagnosis,  67 

Aubert,  on  the  form  of  the  cornea     -  43 

Axis  of  cylinder,  method  of  indicating  its  inclination,  155 

at  right  angles  to  the  faulty  meridian,  57 

B 

Blepharitis,  in  astigmatism,     -  144 

Blows  on  the  eye  producing  astigmatism,      -  150 

Bowman  on  the  shadow-test,  115 

Bravais'  apparatus,     -  85 

method  of  ophthalmoscopic  diagnosis,  109 

Brewster's  description  of  conical  cornea,        -  191 

Burnett's  modification  of  the  ophthalmoscope,  99 


Cassus  used  cylinders  in  1840,  158 

Cataract  extraction,  a  cause  of  astigmatism,  148 

Chorea,  said  to  be  due  to  astigmatism,  143 

Ciliary  muscle,  partial  contraction  of,  -       71,151 

varying  power  of,  69 

inherent  tonicity  of,       -                           -  68 


INDEX.  235 

Clinical  cases,  -     159,  165 

Collecting  optical  systems,  their  office,  8 

Congenital  astigmatism,  147 

Conical  cornea,  diagnosis  of,  192 

lateral  view  of,  192 

Cornea,  Aubert  on  the  form  of,  43 

focal  curve  of,  41 

normal  astigmatism  of,  44 

Harkness  on  the  form  of,  39 

its  form  a  triaxial  ellipsoid,     -  42 

Corneal  and  total  astigmatism,  table  comparing,  -              132 

astigmatism,  history  of,  46,  48 

ellipsoid,  optical  zone  of,         -  43 

ellipsoid,  scleral  zone  of,  43 

irregular  astigmatism,  183 

Correcting  glasses,  sometimes  unsatisfactory,  70 

Correction  of  astigmatism  by  pressing  on  the  sclera,  171 

Couper's  method  of  ophthalmoscopic  diagnosis  in 

astigmatism,  1 10 

Cranium,  shape  of,  influencing  astigmatism,  -  147 

Crossed  cylinders,       -  -       32,  162 

Cuignet  re-introduces  skiascopy,       -  116 

Culbertson's  prisoptometer,   -  84 

Curvature  of  convex  surfaces,  method  of  determining,  125 

Cylinder,  axis  at  right  angles  to  its  refracting  surface,  30 

increase  in  refraction  of  by  rotation,    -  35 

Cylindrical  action  of  spherical  lenses,  -       34,  204 

Cylindrical  lens,  how  formed,  30 

focal  lines  of  23 

refraction  by  31 

Cylindrical  glasses  may  improve    when  no    astig.  is 

present,       -  64 

Cylindrical  glasses  in  kerataconus,     -  198 

Cylindrical  lenses,  forms  of    -  32 

Cystoid  cicatrix,  keratoscopic  appearances  of  185 


236  INDEX. 

D 

Dantel  on  hypermetropia  in  childhood,  69 
Deficiency  in  correction  by  cylinders,  166 
Degree  of  astigmatism,  the  lowest  requiring  correction  1 70 
Dennett,  cylindrical  attachment  to  the  ophthalmo- 
scope, 99 
Dennett's  modification  of  Stokes'  lens,  33 
Diagnosis  of  astigmatism,  illustrative  cases,  57,  59 

best  vision,  the  final  test  of             136 
errors  in,  caused  by  the 

accommodation  -  65 

Diagrams  for  recording  astigmatism,  -  58,  59,  159 

the  axes  of  the  meridians,  -         58,  59 

Difficulty  in  wearing  correcting  glasses,  163 

Dislocation  of  the  lens  producing  astigmatism,  150 

Donders'  first  papers  on  astigmatism,  48 
Drobowolski    on  partial   contraction  of  the  ciliary 

muscle,                      -  71 

E 

Egger,  originates  the  term  skiascopy,  116 

Ellipse   blunter  end  of  16 

definition  of  15 

foci  ot  15 

major  axis  of  15 

minor  axis  of  15 

refraction  by  the  sharper  end  of  17 

sharper  end  of  16 

Ellipses,  refraction  by  16 

Ellipsoids,  biaxial,       -  20 

focal  lines  of,  curved,  23,  25 

no  general  formula  for  their  refraction,  26 

triaxial,  2O 

Elliptical  form  of  the  cornea,  40 

Emmetropic  eye  49 

and  ametropic  eyes  compared,  49 

Eye,  office  of,  as  an  organ  of  sense,  63 


INDEX.  237 

F 

Focal  curve  of  the  normal  cornea,      -  41 

distance,  first,  4 

second,  -                 4 

Focal  distances  of  a  biconvex  lens,  -  -7 

Focal  interval  of  Sturm,  -                22 

circular  section  of  not  in  the  center,     29 

formation  of  -  -28 

Focal  line  of  Sturm's  interval,  anterior  shorter,  -               29 

cylinder  straight,  23 

Focal  plane,  astigmatics    preferably  use  one,  65 

choice  of  by  astigmatics,        -  65 

of  a  triaxial  ellipsoid,                -  22 

of  obliquely  placed  lenses,       -  204 

Foci,  principal,  4 

Forms  of  astigmatism,  relative  frequency  of,  206 

Fundus  of  an  astigmatic  eye  as  seen  by  the  direct 

method,       -  96,  97 

G 

Gavarret,  work  on  optics,       -  10 

Gerson,  on  astigmatism,  46 

Goulier's  account  of  astigmatism,       -  158 

Glass,  crown,  7 

flint,  7 

index  of  refraction  of,  7 

Green,  John,  clock  face  for  diagnosis,  83 

H 

Harkness  on  monochromatic  aberration  of  the  cornea,     39,  41 
Hay,  G.,  on  shortening  of  focus  of  cylinder  by  rotation,          35 
Hays,  Dr.  Isaac,  observation  on  the  correction  of  as- 
tigmatism, 158 
Headache  due  to  astigmatism,  -      141,  142 
Helmholtz's  corneal  measurements,  -  46 
ophthalmometer,  124 
Hirschberg  on  spasm  of  A,    -  70 


238  INDEX. 

Hyperbolic  lenses,      -  199 

Hypermetropic  eye,  -  50 

Hypermetropia,  the  rule  in  childhood,  68 

found  constantly  in  most  lower  animals,  68 

I 

Images,  formed  by  convex  surfaces,  10 

how  formed  by  a  convex  refracting  surface,  -  8 

Inch  system  of  numbering  glasses,    -  1 1 

of  numbering  glasses,  disadvantages  of,  1 1 

always  expressed  in  vulgar  fractions,  13 

how  to  convert  it  into  the  metric,  12 

Intermediate  meridians,  refraction  by,  22 

Inverted  ophthalmoscopic   image,   apparent  size  of 

in  Emmetropia        -  102 

in  hypermetropic  astigmatism,  -     107,  108 

its  size  and  position,    -  -     101,  102 

in  mixed  astigmatism,                             -  107 

in  myopia.  104 

in  myopic  astigmatism,                                        -  106 

size  and  position  of  in  hypermetropia,  103 

Iridectomy  in  irregular  astigmatism,  189 

Iridencleisis,  a  cause  of  astigmatism,                           -  187 

Irregular  astigmatism,                                                      -  177 

normal,  177 

produced  by  accommodation,  -  182 

diagnosis  of,     -  183 

by  the  ophthalmoscope,     183 

treatment  of,     -  1 86 

Irregular  corneal  astigmatism  after  cataract  extraction,         187 

J 
Jager's  inaccurate  drawing  of  the  fundus  of  the  astig. 

eye,             -  95 

J  aval's  astigmometer,  86 

Javal  on  corneal  astigmatism,                           -             -  48 

on  the  form  of  the  cranium   in   astigmatism,  147 

on  lenticular  astigmatism,        -  71 


INDEX.  239 

Javal  and  Schiotz'  ophthalmometer,  124 

Jones  on  astigmatism,  46 

K 

Keratitis  said  to  be  due  to  astigmatism,  144 
Keratoconus,  190 
case  of  193 
a  cause  of  irregular  astigmatism,  148 
operative  treatment  of,  200. 
Keratometry,  exact  meaning  of  the  term       -  124 
its  value  .in  astigmatism  124 
Keratoscope  of  Placido  ;  how  made,  133 
Keratoscopic  appearances  in   irregular  astigmatism,       184,185 
images  in  keratoconus,  -  -       194,195 
Keratoscopy,  false,     -  115 
Keratoscopy  in  the  diagnosis  of  irregular  corneal  as- 
tigmatism, 184 
Keratoscopy,  first  attempt  at,  192 
its  limitations  in  regular    astigmatism,  134 
meaning  and  application  of  the    term,  124 
Keratosis,  191 
Knapp's  combined  method  of  ophthalmoscopic    ex- 
amination, io9 
Knapp,  the  first  to  demonstrate  corneal  astigmatism,  47 

L 

Landolt,  on  the  use  of  atropine  in  determining  astig- 
matism,       -  7° 

Lens,  concave,  action  of  on  light,  7 

convex,  action  of  on  light  7 

Lenses,  collecting       -  3 

different  forms  of,  2,  3 

dispersing  3 

methods  of  numbering,  1 1 

negative,  '    3 

positive,  3 

spherical,  3 

why  so  called,                                          -  2 


24O  INDEX. 

/ 

Lenticular  astigmatism,  149 

forms  of,  150 

neutralizing  corneal  -  71 

causes  of,  45 ,46 

Little,  W.  S.,  test  card  of,      -  56 
Loring's   drawing  of  the    fundus  of  the  astigmatic 

eye  -                                                 -  59 

M 

Mauthner  on  spasm  of  A,       -  70 

McAllister,  made  cylinders  in  1825,   •  158 

Meridians,  intermediate,  22 

Meridians,  principal,  -  21 

the  two  principal  at  right  angles,  20 

Meridian,  vertical  the  more  strongly  curved,  44 
Metric  system,  always  expressed  in  whole  numbers  and 

decimals,     -  13 

how  to  convert  it  into  the  inch,  12 

of  numbering  glasses,  1 1 

Mitchell,  S.  W.,  on  headaches  from  eye-strain,  142 

Monochromatic  aberration,  absence  of,  18 

Mixed  astigmatism,  two  methods  of  correcting,  162 

case  of,  161 

Myopia  as  a  cause  of  astigmatism,    -  144 

Myopic  eye,  -  50 

N 

Near-sightedness,  apparent,  due  to  astigmatism,  144 

Neurasthenic  asthenopia,       -  143 

Nodal  points,  effect  of  cylinders  on,  -  169 

Nordenson  on  corneal  astigmatism,   -  48 

Normal  astigmatism,  demonstration  of,          -  45 

Normal  to  an  ellipse,  how  to  obtain,                            -  16 

O 

Objective  methods,  advantages  of,    -  89 

of  diagnosis,     -  74,  89 

Objective  signs  of  astigmatism,  -      143,  144 


INDHX.  241 

Obliquely  placed  lenses,  cylindrical  action  of,            -  33,  204 
Obstacles  in  the  way  of  an  accurate  diagnosis,  63 
Ochlodes,        -  191 
Oliver,  C.  A.,  disks  for  diagnosis,      -  83 
Ophthalmometer  of  Helmholtz,   practical    disadvan- 
tages of,      -  124 
of  Javal  and  Schiotz,  its  construction,  125, 126, 127, 128, 129 
method  of  using,                                                      -  129,130 
its  optical  basis,  125 
does  not  give  general  ametropia,  131 
Ophthalmometry,  objection  to  the  term,  124 
Ophthalmoscopes,  with  cyl.  attachments,      -             -  99,  100 
Ophthalmoscope  in  the  diagnosis  of  irregular  astigmatism,  183 
in  diagnosis,     -  89 
Ophthalmoscopic  appearance  in  keratoconus,            -  193,195 
examination,  defects  of  in  diagnosing  astigmatism,  93,  94 
different  methods  of,      -  90 
direct  method  in  astigmatism,  -  92,  93 
direct  method  of,  90,  91 
indirect  method  of,  101 
findings   should    be   verified   by 

glasses  and  test-types,  113 

Optical  appliances,  function  of,  2 

Optical  treatment  of  keratoconus,      -  197 

Optics,  elementary  principles  of,  I 

Optometers,    -  84 

Orbit,  influence  of  in  producing  astigmatism,  147 
Over-correcting  combinations  of  sphericals  and  cylinders,     32 

P 

Parallel  rays  of  light,  I 

Parent's  cyl.  attachment  to  the  ophthalmoscope,       -  99 

Partial  accommodation  in  childhood,  140 

causing  astigmatism,                -  71,151 

Phantoscopy,                             -                          -  1 15 

Pickering  and  Williams'  table,  34 

Points,  cardinal,  4.  7 


242  INDEX. 

Points,  nodal,  4,  6 

Point  of  light,  changes  of,  in  astigmatism,    -  75 
Points,  nodal  and  principal,  coincide  in  a  bi-convex 

lens,  7 

Points,  principal,  4 

Placido's  keratoscope,  133 

Planes,  focal,  4 

principal,  4, 5 

Polyopia  monocularis,  180 

Pray  O.,  test  letters  of,  83 

Presbyopia  in  astigmatism,    -  160 

Presbyopia  sometimes  first  makes    astigmatism  felt,  140 

Principal  meridians,  determination  of  the  direction  of               56 

their  inclination  expressed  in  degrees,  57 

points,  same  for  a  simple  refracting  surface,  -                  5 

planes,  same  fora  single  refracting  surface,  -                 5 

Proving  glasses,  171 

by  neutralization,  171 

simultaneous  contrast,  173 

Pupilloscopy,               -  115 

Purves,  Laidlow,  apparatus  for  diagnosis,      -  77 

R 

Rahlmann's  hyperbolic  lenses,  199 

Recording  cases,  method  of  159 

Refraction,  laws  governing,  2 

Refracting-power  of  a  lens,  on  what  it  depends,  7 

Refracting  media  of  the  eye,  38 

Regular  astigmatism  from  keratoconus,  case  of  149 

Retinoscopy,  115 

s 

Schemer's  experiment,  in  diagnosis  of  ametropia,  -               78 

astigmatism,  -                79 

Schoeler's  cyl.  attachment  to    the    ophthalmoscope,  99 
Schmidt-Rimplers'  method  of  ophthaimoscopic  diag- 
nosis,                                                   -             -  -     no,  1 1 1 


INDEX.  243 

Schweigger's  combined  method  of  ophthalmoscopic 

examination,  109 

Sectorial  construction  of  the  lens,      -  178 

Senf,  the  first  to  measure  the  cornea,  46 

Shadow-test,  115 

Skiascopy,  115 

detection  of  principal  meridians  by,  -                            121 

in  diagnosis  of  ametropia,        -  117 

in  the  diagnosis  of  astigmatism,  121 

diagnosis  of  hypermetropia  by,  118 

diagnosis  of  myopia  by,  118 

on  what  it  depends,      -  115 

optical  principles  of,     -  '-     Il6,  117 

use  of  plane  mirror  in,  119 

Sous,  on  diminished  refraction  of  cyl.  by  rotation,    -  35 

Snellen's  fan,  56 

Snyder's  account  of  astigmatism,      -  158 

Spasm  of  accommodation,  illustration  of,  -                           165 

"Spectrum"  of  the  lens,  179 

Spherical  aberration,  excess  of  in  ellipses,  -                             18 

action  of  Stokes'  lens,  83 

glasses  should  always  be  tried  first,  -                             65 

lenses,  how  formed,      -  3 

Sphere-cylinders,       -  32 

Spheroid,  characteristic  refraction  by,  20 

compressed,      -  20 

lorm  of  14 

refraction  by,  19 

Staphyloma  pellucida,  190 

Star-rays,  origin  of,     -  180 

Static  refraction,  examination  of,        -  55 

of  the  eye,     -  66 

Statistical  record,       -  206 

Stenopaic  slit  in  keratoconus,  '197 

in  irregular  astigmatism,  189 

its  use  in  diagnosis,     -  81 

Stokes'  lens,  33 


244  INDEX. 

Strabismus,  operation  for,  a  cause  of  astigmatism,  -             152 

Strawbridge's  apparatus  for  diagnosis,  78 
Sturm's  interval, diffusion  images  greater  on  post,  focal  plane,  29 

sections  of,  at  various  parts,     -  -     27,  28 

Subjective  method  of  diagnosis  74 

Symptoms  of  irregular  astigmatism,      -  188 


Table,  comparative,  of  metric  and  inch  systems,  12 
Tension  of  Eye-ball,  changes  of  corneal  curvature  in,  188 
Thomson's  modification  of  Scheiner's  experiment,    -  80 
Tilted  lenses  in  the  astigmatism  after  cataract  extrac- 
tion,                                                                                 -  171,  205 
Tilting  mirrors,  98 
Trial-frame  of  Meyrowitz,      -  155 
Trial  glasses,  what  a  set  should  contain,  II,  12 
Trial  lenses,   -  1 1 
Triaxial  ellipsoid,  model   of,  21 
normals  to  the  meridians  of,  21 
"skew"  surface  of,    -  21 

u 

Unreliability  of  patients'  statements,  63 

V 

Vision,  diminished,  easily  overlooked  by  patients,     -  139 

Vision,  diminished,  a  subjective  sign  of  astigmatism,  139 

Visual  acuteness  in  astigmatism,                                    -  169,  206 

w 

Wecker's  square  for  testing  for  changes  in  corneal 

curvature,    -                                                                    -  135,  136 

Whewell  first  gave  the  name  astigmatism,     -  158 

Wilde,  on  the  form  of  the  cornea,       -  46 

Women,  relative  frequency  of  astigmatism  in,  206 

Wounds  of  cornea  and  sclera,  causes  of  astigmatism,  148 


INDEX.  245 

Y 

Young's  astigmatism  lenticular,  45 

Young's  case  of  lenticular  astigmatism,  149 

z 

Zehender's  astigmometer,       -  85 


TABLES. 


Table  I. — Inch  and  metric  systems  of  numbering  glasses          12 

Table  II. — Pickering  and  Williams'  tables  showing  the  foci 

of  a  spherical  lens  when  placed  obliquely  34 

Table  III. — Hay's  table,  showing  the  increase  in  refraction 

of  a  cylinder  on  rotation  about  its  axis  -  35 

Table  IV. — Harkness'  table  comparing  the  focus  of  a  normal 

with  spherical  cornea  -  42 

Table  V. — Showing  the  foci  of  the  horizontal  and  vertical 

meridians  in  21  eyes  44 

Table  VI. — Showing  the  difference  in  the  astigmatism  as 

determined  by  Javal's  keratometer  and  test-glasses  132 

Table  VII. — Showing  the  cylindrical  action  of  a  spherical 
lens  placed  obliquely  to  incident  rays,  and  the  ob- 
liquity of  the  focal  plane  205 

Appendix. — Statistical  record  of  806  astigmatic  eyes  -  206 


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